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If $n$ is an integer and $3n+2$ is even, then $n$ is even.
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I am still new to proofs and just starting to get some practice in. Here is what the homework problem asks.
Prove that if $n$ is an integer and $3n+2$ is even, then $n$ is even.
Proof attempt by contradiction: Suppose $3n+2$ is even and $n$ is odd. If $n$ is odd, then $n=2k+1$ for some $k in mathbbZ$. Then, $3n+2=3(2k+1)+2=2(3k)+5$. Since $k in mathbbZ$, then $3k in mathbbZ$. Let $3k=m Rightarrow 3n+2=2m+5$, which is odd. Thus, contradicting our assumption that $3n+2$ is even. $blacksquare$
I feel as if I am missing some steps and/or grazing over something important. Any feedback, tips/suggestions, or words of wisdom would be greatly appreciated. Thank you in advance.
elementary-number-theory proof-verification proof-explanation
asked Jul 28 at 7:15
Ryan
865
add a comment |Â
up vote
3
down vote
favorite
I am still new to proofs and just starting to get some practice in. Here is what the homework problem asks.
Prove that if $n$ is an integer and $3n+2$ is even, then $n$ is even.
Proof attempt by contradiction: Suppose $3n+2$ is even and $n$ is odd. If $n$ is odd, then $n=2k+1$ for some $k in mathbbZ$. Then, $3n+2=3(2k+1)+2=2(3k)+5$. Since $k in mathbbZ$, then $3k in mathbbZ$. Let $3k=m Rightarrow 3n+2=2m+5$, which is odd. Thus, contradicting our assumption that $3n+2$ is even. $blacksquare$
I feel as if I am missing some steps and/or grazing over something important. Any feedback, tips/suggestions, or words of wisdom would be greatly appreciated. Thank you in advance.
elementary-number-theory proof-verification proof-explanation
asked Jul 28 at 7:15
Ryan
865
Normally you use a known fact for your contradiction, not the premise. You didn't use your assumption anywhere. This is better framed as a proof by contrapositive.
– Kaynex
Jul 28 at 7:24
I see. Thank you for your response. How would I state it appropriately if I wanted to prove it by contradiction? Would I say, "assume $n$ is odd."?
– Ryan
Jul 28 at 7:36
2
Remove "Suppose..odd" and start with "Assume that $n$ is odd, then $n=2k+1$ for some $k in mathbbZ$." at the end "Thus, contradicting the assumption that 3n+2 is even." The rest of the proof is fine.
– Robert Z
Jul 28 at 7:44
Great. Thank you for your help!
– Ryan
Jul 28 at 7:50
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I am still new to proofs and just starting to get some practice in. Here is what the homework problem asks.
Prove that if $n$ is an integer and $3n+2$ is even, then $n$ is even.
Proof attempt by contradiction: Suppose $3n+2$ is even and $n$ is odd. If $n$ is odd, then $n=2k+1$ for some $k in mathbbZ$. Then, $3n+2=3(2k+1)+2=2(3k)+5$. Since $k in mathbbZ$, then $3k in mathbbZ$. Let $3k=m Rightarrow 3n+2=2m+5$, which is odd. Thus, contradicting our assumption that $3n+2$ is even. $blacksquare$
I feel as if I am missing some steps and/or grazing over something important. Any feedback, tips/suggestions, or words of wisdom would be greatly appreciated. Thank you in advance.
elementary-number-theory proof-verification proof-explanation
asked Jul 28 at 7:15
Ryan
865
I am still new to proofs and just starting to get some practice in. Here is what the homework problem asks.
Prove that if $n$ is an integer and $3n+2$ is even, then $n$ is even.
Proof attempt by contradiction: Suppose $3n+2$ is even and $n$ is odd. If $n$ is odd, then $n=2k+1$ for some $k in mathbbZ$. Then, $3n+2=3(2k+1)+2=2(3k)+5$. Since $k in mathbbZ$, then $3k in mathbbZ$. Let $3k=m Rightarrow 3n+2=2m+5$, which is odd. Thus, contradicting our assumption that $3n+2$ is even. $blacksquare$
I feel as if I am missing some steps and/or grazing over something important. Any feedback, tips/suggestions, or words of wisdom would be greatly appreciated. Thank you in advance.
elementary-number-theory proof-verification proof-explanation
asked Jul 28 at 7:15
Ryan
865
asked Jul 28 at 7:15
Ryan
865
asked Jul 28 at 7:15
Ryan
865
asked Jul 28 at 7:15
Ryan
865
865
Normally you use a known fact for your contradiction, not the premise. You didn't use your assumption anywhere. This is better framed as a proof by contrapositive.
– Kaynex
Jul 28 at 7:24
I see. Thank you for your response. How would I state it appropriately if I wanted to prove it by contradiction? Would I say, "assume $n$ is odd."?
– Ryan
Jul 28 at 7:36
2
Remove "Suppose..odd" and start with "Assume that $n$ is odd, then $n=2k+1$ for some $k in mathbbZ$." at the end "Thus, contradicting the assumption that 3n+2 is even." The rest of the proof is fine.
– Robert Z
Jul 28 at 7:44
Great. Thank you for your help!
– Ryan
Jul 28 at 7:50
add a comment |Â
Normally you use a known fact for your contradiction, not the premise. You didn't use your assumption anywhere. This is better framed as a proof by contrapositive.
– Kaynex
Jul 28 at 7:24
I see. Thank you for your response. How would I state it appropriately if I wanted to prove it by contradiction? Would I say, "assume $n$ is odd."?
– Ryan
Jul 28 at 7:36
2
Remove "Suppose..odd" and start with "Assume that $n$ is odd, then $n=2k+1$ for some $k in mathbbZ$." at the end "Thus, contradicting the assumption that 3n+2 is even." The rest of the proof is fine.
– Robert Z
Jul 28 at 7:44
Great. Thank you for your help!
– Ryan
Jul 28 at 7:50
Normally you use a known fact for your contradiction, not the premise. You didn't use your assumption anywhere. This is better framed as a proof by contrapositive.
– Kaynex
Jul 28 at 7:24
Normally you use a known fact for your contradiction, not the premise. You didn't use your assumption anywhere. This is better framed as a proof by contrapositive.
– Kaynex
Jul 28 at 7:24
I see. Thank you for your response. How would I state it appropriately if I wanted to prove it by contradiction? Would I say, "assume $n$ is odd."?
– Ryan
Jul 28 at 7:36
I see. Thank you for your response. How would I state it appropriately if I wanted to prove it by contradiction? Would I say, "assume $n$ is odd."?
– Ryan
Jul 28 at 7:36
2
2
Remove "Suppose..odd" and start with "Assume that $n$ is odd, then $n=2k+1$ for some $k in mathbbZ$." at the end "Thus, contradicting the assumption that 3n+2 is even." The rest of the proof is fine.
– Robert Z
Jul 28 at 7:44
Remove "Suppose..odd" and start with "Assume that $n$ is odd, then $n=2k+1$ for some $k in mathbbZ$." at the end "Thus, contradicting the assumption that 3n+2 is even." The rest of the proof is fine.
– Robert Z
Jul 28 at 7:44
Great. Thank you for your help!
– Ryan
Jul 28 at 7:50
Great. Thank you for your help!
– Ryan
Jul 28 at 7:50
add a comment |Â
4 Answers
4
active
oldest
votes
up vote
3
down vote
accepted
Yes, your proof is OK.
Say $n$ is odd, so $3n$ is odd, so $3n+2$ is odd, a contradiction.
Or you can do like this: since $2mid 3n+2$ we have $2mid (3n+2)-2 = 3n$. But $gcd(3,2)=1$ so $2mid n$.
answered Jul 28 at 7:17
greedoid
26.1k93473
Sorry, we haven't covered too much on gcd and the method you are suggesting. How can we assume $2$ divides $3n+2$?
– Ryan
Jul 28 at 7:27
2
Because $3n+2$ is even.
– greedoid
Jul 28 at 7:36
add a comment |Â
up vote
2
down vote
Your proof by contradiction is fine. This is a direct proof: if $3n+2$ is even then there is $kinmathbbZ$ such that $3n+2=2k$. Hence, since $n$ is an integer, it follows that
$$n=2k-2-2n=2(underbracek−1−n_in mathbbZ )$$
which means that $n$ is even.
answered Jul 28 at 7:22
Robert Z
83.8k954122
Thank you for your help. I understand how you arrived at $2k-2$, but how do we get $-2n$? Sorry, if I am lacking on my algebra. It is a little late here.
– Ryan
Jul 28 at 7:30
1
We have that $3n+2=n+2n+2$ and then we move $2n+2$ to the other side.
– Robert Z
Jul 28 at 7:34
Ah, I see. Thanks for the help!
– Ryan
Jul 28 at 7:39
add a comment |Â
up vote
1
down vote
Yes it is a correct proof by contradiction, more simply we can conclude from here
$$2(3k)+5=2(3k)+4+1=2(3k+2)+1$$
but it is really a detail.
answered Jul 28 at 7:20
gimusi
64.8k73483
Thank you so much for your feedback. I am happy to hear I am starting to get a little more comfortable with it.
– Ryan
Jul 28 at 7:26
Also, I was trying to do some algebra and manipulate it, but I couldn't figure it out. Thank you for the clarification!
– Ryan
Jul 28 at 7:33
You are welcome! Bye
– gimusi
Jul 28 at 7:36
add a comment |Â
up vote
1
down vote
If $3n+2$ is even, then $3n+2equiv0 mod 2Rightarrow 3nequiv0 mod 2$.
Where $ninmathbbZ_2=0,1 $.
If $nequiv1 mod 2$ then $3(1)equiv0 mod 2$ this is a contradiction, since $1not equiv0 mod 2$.
Therefore $nequiv 0 mod 2$ then $n$ is even.
answered Jul 28 at 15:24
Julio Trujillo Gonzalez
575
Thank you for your response. We have not covered modulo ideas, yet, so I am having a little hard time understanding your solution.
– Ryan
Jul 28 at 17:05
Don't have problem, since $aequiv b mod m Leftrightarrow mmid (a-b) Leftrightarrow a-b=mq+r$, such that $0leq r <m$ then $rin 0,1,2,cdots, m-1 $
– Julio Trujillo Gonzalez
Jul 28 at 17:42
add a comment |Â
4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Yes, your proof is OK.
Say $n$ is odd, so $3n$ is odd, so $3n+2$ is odd, a contradiction.
Or you can do like this: since $2mid 3n+2$ we have $2mid (3n+2)-2 = 3n$. But $gcd(3,2)=1$ so $2mid n$.
answered Jul 28 at 7:17
greedoid
26.1k93473
Sorry, we haven't covered too much on gcd and the method you are suggesting. How can we assume $2$ divides $3n+2$?
– Ryan
Jul 28 at 7:27
2
Because $3n+2$ is even.
– greedoid
Jul 28 at 7:36
add a comment |Â
up vote
3
down vote
accepted
Yes, your proof is OK.
Say $n$ is odd, so $3n$ is odd, so $3n+2$ is odd, a contradiction.
Or you can do like this: since $2mid 3n+2$ we have $2mid (3n+2)-2 = 3n$. But $gcd(3,2)=1$ so $2mid n$.
answered Jul 28 at 7:17
greedoid
26.1k93473
Sorry, we haven't covered too much on gcd and the method you are suggesting. How can we assume $2$ divides $3n+2$?
– Ryan
Jul 28 at 7:27
2
Because $3n+2$ is even.
– greedoid
Jul 28 at 7:36
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Yes, your proof is OK.
Say $n$ is odd, so $3n$ is odd, so $3n+2$ is odd, a contradiction.
Or you can do like this: since $2mid 3n+2$ we have $2mid (3n+2)-2 = 3n$. But $gcd(3,2)=1$ so $2mid n$.
answered Jul 28 at 7:17
greedoid
26.1k93473
Yes, your proof is OK.
Say $n$ is odd, so $3n$ is odd, so $3n+2$ is odd, a contradiction.
Or you can do like this: since $2mid 3n+2$ we have $2mid (3n+2)-2 = 3n$. But $gcd(3,2)=1$ so $2mid n$.
answered Jul 28 at 7:17
greedoid
26.1k93473
edited Jul 28 at 7:22
answered Jul 28 at 7:17
greedoid
26.1k93473
answered Jul 28 at 7:17
greedoid
26.1k93473
answered Jul 28 at 7:17
greedoid
26.1k93473
26.1k93473
Sorry, we haven't covered too much on gcd and the method you are suggesting. How can we assume $2$ divides $3n+2$?
– Ryan
Jul 28 at 7:27
2
Because $3n+2$ is even.
– greedoid
Jul 28 at 7:36
add a comment |Â
Sorry, we haven't covered too much on gcd and the method you are suggesting. How can we assume $2$ divides $3n+2$?
– Ryan
Jul 28 at 7:27
2
Because $3n+2$ is even.
– greedoid
Jul 28 at 7:36
Sorry, we haven't covered too much on gcd and the method you are suggesting. How can we assume $2$ divides $3n+2$?
– Ryan
Jul 28 at 7:27
Sorry, we haven't covered too much on gcd and the method you are suggesting. How can we assume $2$ divides $3n+2$?
– Ryan
Jul 28 at 7:27
2
2
Because $3n+2$ is even.
– greedoid
Jul 28 at 7:36
Because $3n+2$ is even.
– greedoid
Jul 28 at 7:36
add a comment |Â
up vote
2
down vote
Your proof by contradiction is fine. This is a direct proof: if $3n+2$ is even then there is $kinmathbbZ$ such that $3n+2=2k$. Hence, since $n$ is an integer, it follows that
$$n=2k-2-2n=2(underbracek−1−n_in mathbbZ )$$
which means that $n$ is even.
answered Jul 28 at 7:22
Robert Z
83.8k954122
Thank you for your help. I understand how you arrived at $2k-2$, but how do we get $-2n$? Sorry, if I am lacking on my algebra. It is a little late here.
– Ryan
Jul 28 at 7:30
1
We have that $3n+2=n+2n+2$ and then we move $2n+2$ to the other side.
– Robert Z
Jul 28 at 7:34
Ah, I see. Thanks for the help!
– Ryan
Jul 28 at 7:39
add a comment |Â
up vote
2
down vote
Your proof by contradiction is fine. This is a direct proof: if $3n+2$ is even then there is $kinmathbbZ$ such that $3n+2=2k$. Hence, since $n$ is an integer, it follows that
$$n=2k-2-2n=2(underbracek−1−n_in mathbbZ )$$
which means that $n$ is even.
answered Jul 28 at 7:22
Robert Z
83.8k954122
Thank you for your help. I understand how you arrived at $2k-2$, but how do we get $-2n$? Sorry, if I am lacking on my algebra. It is a little late here.
– Ryan
Jul 28 at 7:30
1
We have that $3n+2=n+2n+2$ and then we move $2n+2$ to the other side.
– Robert Z
Jul 28 at 7:34
Ah, I see. Thanks for the help!
– Ryan
Jul 28 at 7:39
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Your proof by contradiction is fine. This is a direct proof: if $3n+2$ is even then there is $kinmathbbZ$ such that $3n+2=2k$. Hence, since $n$ is an integer, it follows that
$$n=2k-2-2n=2(underbracek−1−n_in mathbbZ )$$
which means that $n$ is even.
answered Jul 28 at 7:22
Robert Z
83.8k954122
Your proof by contradiction is fine. This is a direct proof: if $3n+2$ is even then there is $kinmathbbZ$ such that $3n+2=2k$. Hence, since $n$ is an integer, it follows that
$$n=2k-2-2n=2(underbracek−1−n_in mathbbZ )$$
which means that $n$ is even.
answered Jul 28 at 7:22
Robert Z
83.8k954122
edited Jul 28 at 7:35
answered Jul 28 at 7:22
Robert Z
83.8k954122
answered Jul 28 at 7:22
Robert Z
83.8k954122
answered Jul 28 at 7:22
Robert Z
83.8k954122
83.8k954122
Thank you for your help. I understand how you arrived at $2k-2$, but how do we get $-2n$? Sorry, if I am lacking on my algebra. It is a little late here.
– Ryan
Jul 28 at 7:30
1
We have that $3n+2=n+2n+2$ and then we move $2n+2$ to the other side.
– Robert Z
Jul 28 at 7:34
Ah, I see. Thanks for the help!
– Ryan
Jul 28 at 7:39
add a comment |Â
Thank you for your help. I understand how you arrived at $2k-2$, but how do we get $-2n$? Sorry, if I am lacking on my algebra. It is a little late here.
– Ryan
Jul 28 at 7:30
1
We have that $3n+2=n+2n+2$ and then we move $2n+2$ to the other side.
– Robert Z
Jul 28 at 7:34
Ah, I see. Thanks for the help!
– Ryan
Jul 28 at 7:39
Thank you for your help. I understand how you arrived at $2k-2$, but how do we get $-2n$? Sorry, if I am lacking on my algebra. It is a little late here.
– Ryan
Jul 28 at 7:30
Thank you for your help. I understand how you arrived at $2k-2$, but how do we get $-2n$? Sorry, if I am lacking on my algebra. It is a little late here.
– Ryan
Jul 28 at 7:30
1
1
We have that $3n+2=n+2n+2$ and then we move $2n+2$ to the other side.
– Robert Z
Jul 28 at 7:34
We have that $3n+2=n+2n+2$ and then we move $2n+2$ to the other side.
– Robert Z
Jul 28 at 7:34
Ah, I see. Thanks for the help!
– Ryan
Jul 28 at 7:39
Ah, I see. Thanks for the help!
– Ryan
Jul 28 at 7:39
add a comment |Â
up vote
1
down vote
Yes it is a correct proof by contradiction, more simply we can conclude from here
$$2(3k)+5=2(3k)+4+1=2(3k+2)+1$$
but it is really a detail.
answered Jul 28 at 7:20
gimusi
64.8k73483
Thank you so much for your feedback. I am happy to hear I am starting to get a little more comfortable with it.
– Ryan
Jul 28 at 7:26
Also, I was trying to do some algebra and manipulate it, but I couldn't figure it out. Thank you for the clarification!
– Ryan
Jul 28 at 7:33
You are welcome! Bye
– gimusi
Jul 28 at 7:36
add a comment |Â
up vote
1
down vote
Yes it is a correct proof by contradiction, more simply we can conclude from here
$$2(3k)+5=2(3k)+4+1=2(3k+2)+1$$
but it is really a detail.
answered Jul 28 at 7:20
gimusi
64.8k73483
Thank you so much for your feedback. I am happy to hear I am starting to get a little more comfortable with it.
– Ryan
Jul 28 at 7:26
Also, I was trying to do some algebra and manipulate it, but I couldn't figure it out. Thank you for the clarification!
– Ryan
Jul 28 at 7:33
You are welcome! Bye
– gimusi
Jul 28 at 7:36
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Yes it is a correct proof by contradiction, more simply we can conclude from here
$$2(3k)+5=2(3k)+4+1=2(3k+2)+1$$
but it is really a detail.
answered Jul 28 at 7:20
gimusi
64.8k73483
Yes it is a correct proof by contradiction, more simply we can conclude from here
$$2(3k)+5=2(3k)+4+1=2(3k+2)+1$$
but it is really a detail.
answered Jul 28 at 7:20
gimusi
64.8k73483
answered Jul 28 at 7:20
gimusi
64.8k73483
answered Jul 28 at 7:20
gimusi
64.8k73483
answered Jul 28 at 7:20
gimusi
64.8k73483
64.8k73483
Thank you so much for your feedback. I am happy to hear I am starting to get a little more comfortable with it.
– Ryan
Jul 28 at 7:26
Also, I was trying to do some algebra and manipulate it, but I couldn't figure it out. Thank you for the clarification!
– Ryan
Jul 28 at 7:33
You are welcome! Bye
– gimusi
Jul 28 at 7:36
add a comment |Â
Thank you so much for your feedback. I am happy to hear I am starting to get a little more comfortable with it.
– Ryan
Jul 28 at 7:26
Also, I was trying to do some algebra and manipulate it, but I couldn't figure it out. Thank you for the clarification!
– Ryan
Jul 28 at 7:33
You are welcome! Bye
– gimusi
Jul 28 at 7:36
Thank you so much for your feedback. I am happy to hear I am starting to get a little more comfortable with it.
– Ryan
Jul 28 at 7:26
Thank you so much for your feedback. I am happy to hear I am starting to get a little more comfortable with it.
– Ryan
Jul 28 at 7:26
Also, I was trying to do some algebra and manipulate it, but I couldn't figure it out. Thank you for the clarification!
– Ryan
Jul 28 at 7:33
Also, I was trying to do some algebra and manipulate it, but I couldn't figure it out. Thank you for the clarification!
– Ryan
Jul 28 at 7:33
You are welcome! Bye
– gimusi
Jul 28 at 7:36
You are welcome! Bye
– gimusi
Jul 28 at 7:36
add a comment |Â
up vote
1
down vote
If $3n+2$ is even, then $3n+2equiv0 mod 2Rightarrow 3nequiv0 mod 2$.
Where $ninmathbbZ_2=0,1 $.
If $nequiv1 mod 2$ then $3(1)equiv0 mod 2$ this is a contradiction, since $1not equiv0 mod 2$.
Therefore $nequiv 0 mod 2$ then $n$ is even.
answered Jul 28 at 15:24
Julio Trujillo Gonzalez
575
Thank you for your response. We have not covered modulo ideas, yet, so I am having a little hard time understanding your solution.
– Ryan
Jul 28 at 17:05
Don't have problem, since $aequiv b mod m Leftrightarrow mmid (a-b) Leftrightarrow a-b=mq+r$, such that $0leq r <m$ then $rin 0,1,2,cdots, m-1 $
– Julio Trujillo Gonzalez
Jul 28 at 17:42
add a comment |Â
up vote
1
down vote
If $3n+2$ is even, then $3n+2equiv0 mod 2Rightarrow 3nequiv0 mod 2$.
Where $ninmathbbZ_2=0,1 $.
If $nequiv1 mod 2$ then $3(1)equiv0 mod 2$ this is a contradiction, since $1not equiv0 mod 2$.
Therefore $nequiv 0 mod 2$ then $n$ is even.
answered Jul 28 at 15:24
Julio Trujillo Gonzalez
575
Thank you for your response. We have not covered modulo ideas, yet, so I am having a little hard time understanding your solution.
– Ryan
Jul 28 at 17:05
Don't have problem, since $aequiv b mod m Leftrightarrow mmid (a-b) Leftrightarrow a-b=mq+r$, such that $0leq r <m$ then $rin 0,1,2,cdots, m-1 $
– Julio Trujillo Gonzalez
Jul 28 at 17:42
add a comment |Â
up vote
1
down vote
up vote
1
down vote
If $3n+2$ is even, then $3n+2equiv0 mod 2Rightarrow 3nequiv0 mod 2$.
Where $ninmathbbZ_2=0,1 $.
If $nequiv1 mod 2$ then $3(1)equiv0 mod 2$ this is a contradiction, since $1not equiv0 mod 2$.
Therefore $nequiv 0 mod 2$ then $n$ is even.
answered Jul 28 at 15:24
Julio Trujillo Gonzalez
575
If $3n+2$ is even, then $3n+2equiv0 mod 2Rightarrow 3nequiv0 mod 2$.
Where $ninmathbbZ_2=0,1 $.
If $nequiv1 mod 2$ then $3(1)equiv0 mod 2$ this is a contradiction, since $1not equiv0 mod 2$.
Therefore $nequiv 0 mod 2$ then $n$ is even.
answered Jul 28 at 15:24
Julio Trujillo Gonzalez
575
answered Jul 28 at 15:24
Julio Trujillo Gonzalez
575
answered Jul 28 at 15:24
Julio Trujillo Gonzalez
575
answered Jul 28 at 15:24
Julio Trujillo Gonzalez
575
575
Thank you for your response. We have not covered modulo ideas, yet, so I am having a little hard time understanding your solution.
– Ryan
Jul 28 at 17:05
Don't have problem, since $aequiv b mod m Leftrightarrow mmid (a-b) Leftrightarrow a-b=mq+r$, such that $0leq r <m$ then $rin 0,1,2,cdots, m-1 $
– Julio Trujillo Gonzalez
Jul 28 at 17:42
add a comment |Â
Thank you for your response. We have not covered modulo ideas, yet, so I am having a little hard time understanding your solution.
– Ryan
Jul 28 at 17:05
Don't have problem, since $aequiv b mod m Leftrightarrow mmid (a-b) Leftrightarrow a-b=mq+r$, such that $0leq r <m$ then $rin 0,1,2,cdots, m-1 $
– Julio Trujillo Gonzalez
Jul 28 at 17:42
Thank you for your response. We have not covered modulo ideas, yet, so I am having a little hard time understanding your solution.
– Ryan
Jul 28 at 17:05
Thank you for your response. We have not covered modulo ideas, yet, so I am having a little hard time understanding your solution.
– Ryan
Jul 28 at 17:05
Don't have problem, since $aequiv b mod m Leftrightarrow mmid (a-b) Leftrightarrow a-b=mq+r$, such that $0leq r <m$ then $rin 0,1,2,cdots, m-1 $
– Julio Trujillo Gonzalez
Jul 28 at 17:42
Don't have problem, since $aequiv b mod m Leftrightarrow mmid (a-b) Leftrightarrow a-b=mq+r$, such that $0leq r <m$ then $rin 0,1,2,cdots, m-1 $
– Julio Trujillo Gonzalez
Jul 28 at 17:42
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Normally you use a known fact for your contradiction, not the premise. You didn't use your assumption anywhere. This is better framed as a proof by contrapositive.
– Kaynex
Jul 28 at 7:24
I see. Thank you for your response. How would I state it appropriately if I wanted to prove it by contradiction? Would I say, "assume $n$ is odd."?
– Ryan
Jul 28 at 7:36
2
Remove "Suppose..odd" and start with "Assume that $n$ is odd, then $n=2k+1$ for some $k in mathbbZ$." at the end "Thus, contradicting the assumption that 3n+2 is even." The rest of the proof is fine.
– Robert Z
Jul 28 at 7:44
Great. Thank you for your help!
– Ryan
Jul 28 at 7:50