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How to solve this problem using modular arithmetics? $276A$ is divisible by $3$ without a remainder. Then determine the values $A$ can take. [closed]
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$276A$ is divisible by $3$ without a remainder. Then determine the values $A$ can take.
I want to solve this problem using modular arithmetics.
$$276A equiv 0 space space (textmod space 3)$$
However, I don't have any idea concerning how to proceed.
Regards!
divisibility
asked Aug 6 at 11:13
Hamilton
967
closed as off-topic by amWhy, Xander Henderson, Taroccoesbrocco, hardmath, Jendrik Stelzner Aug 10 at 3:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Taroccoesbrocco, hardmath, Jendrik Stelzner
add a comment |Â
up vote
-1
down vote
favorite
$276A$ is divisible by $3$ without a remainder. Then determine the values $A$ can take.
I want to solve this problem using modular arithmetics.
$$276A equiv 0 space space (textmod space 3)$$
However, I don't have any idea concerning how to proceed.
Regards!
divisibility
asked Aug 6 at 11:13
Hamilton
967
closed as off-topic by amWhy, Xander Henderson, Taroccoesbrocco, hardmath, Jendrik Stelzner Aug 10 at 3:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Taroccoesbrocco, hardmath, Jendrik Stelzner
Hint: the given equation leads to the fact that $276A = 3n$ for some whole number $n$. Maybe from this you can get some idea ...
– Matti P.
Aug 6 at 11:16
It needs to be assumed that $A$ is an integer in order to apply modular arithmetic in an elementary fashion. It seems possible that some discussion preceding this assigned exercise has been omitted in transcribing it here.
– hardmath
Aug 10 at 2:25
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
$276A$ is divisible by $3$ without a remainder. Then determine the values $A$ can take.
I want to solve this problem using modular arithmetics.
$$276A equiv 0 space space (textmod space 3)$$
However, I don't have any idea concerning how to proceed.
Regards!
divisibility
asked Aug 6 at 11:13
Hamilton
967
$276A$ is divisible by $3$ without a remainder. Then determine the values $A$ can take.
I want to solve this problem using modular arithmetics.
$$276A equiv 0 space space (textmod space 3)$$
However, I don't have any idea concerning how to proceed.
Regards!
divisibility
asked Aug 6 at 11:13
Hamilton
967
asked Aug 6 at 11:13
Hamilton
967
asked Aug 6 at 11:13
Hamilton
967
asked Aug 6 at 11:13
Hamilton
967
967
closed as off-topic by amWhy, Xander Henderson, Taroccoesbrocco, hardmath, Jendrik Stelzner Aug 10 at 3:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Taroccoesbrocco, hardmath, Jendrik Stelzner
closed as off-topic by amWhy, Xander Henderson, Taroccoesbrocco, hardmath, Jendrik Stelzner Aug 10 at 3:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Taroccoesbrocco, hardmath, Jendrik Stelzner
Hint: the given equation leads to the fact that $276A = 3n$ for some whole number $n$. Maybe from this you can get some idea ...
– Matti P.
Aug 6 at 11:16
It needs to be assumed that $A$ is an integer in order to apply modular arithmetic in an elementary fashion. It seems possible that some discussion preceding this assigned exercise has been omitted in transcribing it here.
– hardmath
Aug 10 at 2:25
add a comment |Â
Hint: the given equation leads to the fact that $276A = 3n$ for some whole number $n$. Maybe from this you can get some idea ...
– Matti P.
Aug 6 at 11:16
It needs to be assumed that $A$ is an integer in order to apply modular arithmetic in an elementary fashion. It seems possible that some discussion preceding this assigned exercise has been omitted in transcribing it here.
– hardmath
Aug 10 at 2:25
Hint: the given equation leads to the fact that $276A = 3n$ for some whole number $n$. Maybe from this you can get some idea ...
– Matti P.
Aug 6 at 11:16
Hint: the given equation leads to the fact that $276A = 3n$ for some whole number $n$. Maybe from this you can get some idea ...
– Matti P.
Aug 6 at 11:16
It needs to be assumed that $A$ is an integer in order to apply modular arithmetic in an elementary fashion. It seems possible that some discussion preceding this assigned exercise has been omitted in transcribing it here.
– hardmath
Aug 10 at 2:25
It needs to be assumed that $A$ is an integer in order to apply modular arithmetic in an elementary fashion. It seems possible that some discussion preceding this assigned exercise has been omitted in transcribing it here.
– hardmath
Aug 10 at 2:25
add a comment |Â
2 Answers
2
active
oldest
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up vote
0
down vote
Since already $276=2^2cdot 3cdot 23equiv 0bmod 3$, we have
$$
276Aequiv 0bmod 3
$$
for all integers $A$. So $A$ can take arbitrary integer values.
answered Aug 6 at 11:16
Dietrich Burde
74.8k64185
Maybe we can extend $A$ to be a rational number? Just an idea ...
– Matti P.
Aug 6 at 11:20
@MattiP. What you mentioned is truly right. However, we will need to consider that $Ain mathbbZ$
– Hamilton
Aug 6 at 11:21
Can you also explain it further?
– Hamilton
Aug 6 at 11:23
add a comment |Â
up vote
0
down vote
If 276A is divisible by 3 then there are a number of things we can say such as:
- Since 276 is divisible by 3, A can take any integer value
- Further, since 276 is divisible by 6, A could be not only any integer value but also any number of the form: $A=n+frac 1 2$ where "n" is any integer.
- $A=n+frac m 92$, where n & m are any integers, also produces a multiple of 3 because $frac 27692=3$. (The previous case is a special case of this one.)
- etc - more could be added but this gives the general idea.
answered Aug 6 at 11:39
Dr Peter McGowan
4737
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Since already $276=2^2cdot 3cdot 23equiv 0bmod 3$, we have
$$
276Aequiv 0bmod 3
$$
for all integers $A$. So $A$ can take arbitrary integer values.
answered Aug 6 at 11:16
Dietrich Burde
74.8k64185
Maybe we can extend $A$ to be a rational number? Just an idea ...
– Matti P.
Aug 6 at 11:20
@MattiP. What you mentioned is truly right. However, we will need to consider that $Ain mathbbZ$
– Hamilton
Aug 6 at 11:21
Can you also explain it further?
– Hamilton
Aug 6 at 11:23
add a comment |Â
up vote
0
down vote
Since already $276=2^2cdot 3cdot 23equiv 0bmod 3$, we have
$$
276Aequiv 0bmod 3
$$
for all integers $A$. So $A$ can take arbitrary integer values.
answered Aug 6 at 11:16
Dietrich Burde
74.8k64185
Maybe we can extend $A$ to be a rational number? Just an idea ...
– Matti P.
Aug 6 at 11:20
@MattiP. What you mentioned is truly right. However, we will need to consider that $Ain mathbbZ$
– Hamilton
Aug 6 at 11:21
Can you also explain it further?
– Hamilton
Aug 6 at 11:23
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Since already $276=2^2cdot 3cdot 23equiv 0bmod 3$, we have
$$
276Aequiv 0bmod 3
$$
for all integers $A$. So $A$ can take arbitrary integer values.
answered Aug 6 at 11:16
Dietrich Burde
74.8k64185
Since already $276=2^2cdot 3cdot 23equiv 0bmod 3$, we have
$$
276Aequiv 0bmod 3
$$
for all integers $A$. So $A$ can take arbitrary integer values.
answered Aug 6 at 11:16
Dietrich Burde
74.8k64185
answered Aug 6 at 11:16
Dietrich Burde
74.8k64185
answered Aug 6 at 11:16
Dietrich Burde
74.8k64185
answered Aug 6 at 11:16
Dietrich Burde
74.8k64185
74.8k64185
Maybe we can extend $A$ to be a rational number? Just an idea ...
– Matti P.
Aug 6 at 11:20
@MattiP. What you mentioned is truly right. However, we will need to consider that $Ain mathbbZ$
– Hamilton
Aug 6 at 11:21
Can you also explain it further?
– Hamilton
Aug 6 at 11:23
add a comment |Â
Maybe we can extend $A$ to be a rational number? Just an idea ...
– Matti P.
Aug 6 at 11:20
@MattiP. What you mentioned is truly right. However, we will need to consider that $Ain mathbbZ$
– Hamilton
Aug 6 at 11:21
Can you also explain it further?
– Hamilton
Aug 6 at 11:23
Maybe we can extend $A$ to be a rational number? Just an idea ...
– Matti P.
Aug 6 at 11:20
Maybe we can extend $A$ to be a rational number? Just an idea ...
– Matti P.
Aug 6 at 11:20
@MattiP. What you mentioned is truly right. However, we will need to consider that $Ain mathbbZ$
– Hamilton
Aug 6 at 11:21
@MattiP. What you mentioned is truly right. However, we will need to consider that $Ain mathbbZ$
– Hamilton
Aug 6 at 11:21
Can you also explain it further?
– Hamilton
Aug 6 at 11:23
Can you also explain it further?
– Hamilton
Aug 6 at 11:23
add a comment |Â
up vote
0
down vote
If 276A is divisible by 3 then there are a number of things we can say such as:
- Since 276 is divisible by 3, A can take any integer value
- Further, since 276 is divisible by 6, A could be not only any integer value but also any number of the form: $A=n+frac 1 2$ where "n" is any integer.
- $A=n+frac m 92$, where n & m are any integers, also produces a multiple of 3 because $frac 27692=3$. (The previous case is a special case of this one.)
- etc - more could be added but this gives the general idea.
answered Aug 6 at 11:39
Dr Peter McGowan
4737
add a comment |Â
up vote
0
down vote
If 276A is divisible by 3 then there are a number of things we can say such as:
- Since 276 is divisible by 3, A can take any integer value
- Further, since 276 is divisible by 6, A could be not only any integer value but also any number of the form: $A=n+frac 1 2$ where "n" is any integer.
- $A=n+frac m 92$, where n & m are any integers, also produces a multiple of 3 because $frac 27692=3$. (The previous case is a special case of this one.)
- etc - more could be added but this gives the general idea.
answered Aug 6 at 11:39
Dr Peter McGowan
4737
add a comment |Â
up vote
0
down vote
up vote
0
down vote
If 276A is divisible by 3 then there are a number of things we can say such as:
- Since 276 is divisible by 3, A can take any integer value
- Further, since 276 is divisible by 6, A could be not only any integer value but also any number of the form: $A=n+frac 1 2$ where "n" is any integer.
- $A=n+frac m 92$, where n & m are any integers, also produces a multiple of 3 because $frac 27692=3$. (The previous case is a special case of this one.)
- etc - more could be added but this gives the general idea.
answered Aug 6 at 11:39
Dr Peter McGowan
4737
If 276A is divisible by 3 then there are a number of things we can say such as:
- Since 276 is divisible by 3, A can take any integer value
- Further, since 276 is divisible by 6, A could be not only any integer value but also any number of the form: $A=n+frac 1 2$ where "n" is any integer.
- $A=n+frac m 92$, where n & m are any integers, also produces a multiple of 3 because $frac 27692=3$. (The previous case is a special case of this one.)
- etc - more could be added but this gives the general idea.
answered Aug 6 at 11:39
Dr Peter McGowan
4737
answered Aug 6 at 11:39
Dr Peter McGowan
4737
answered Aug 6 at 11:39
Dr Peter McGowan
4737
answered Aug 6 at 11:39
Dr Peter McGowan
4737
4737
add a comment |Â
add a comment |Â
Hint: the given equation leads to the fact that $276A = 3n$ for some whole number $n$. Maybe from this you can get some idea ...
– Matti P.
Aug 6 at 11:16
It needs to be assumed that $A$ is an integer in order to apply modular arithmetic in an elementary fashion. It seems possible that some discussion preceding this assigned exercise has been omitted in transcribing it here.
– hardmath
Aug 10 at 2:25