what are the conditions when $a^n+b^n$ is divisible by $a-b$

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what are the conditions when $a^n+b^n$ is divisible by $a-b$? I know that it is divisible by $a+b $ when $n $ is odd but I want to find out when it is divisible by $a-b$ and when it is not.




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locked by Michael Greinecker♦ yesterday


This question is locked in view of our policy about contest questions. Questions originating from active contests are locked for the duration of the contest, with answers hidden from view by soft-deletion. Please see the comments below for references to the originating contest.














  • For fixed $a,b$ or all $a,b$?
    – lhf
    2 days ago






  • 2




    when $2b^n equiv 0 pmoda-b$, e.g. $a=2b$
    – rtybase
    2 days ago







  • 3




    I'm voting to close this question as off-topic because it is taken from an on going programming competition, codechef.com/AUG18B/problems/GCDMOD
    – lulu
    2 days ago










  • In addition to voting to close this as off-topic, I have flagged it for moderator review, as per the contest problem guidelines.
    – Xander Henderson
    yesterday















up vote
0
down vote

favorite












what are the conditions when $a^n+b^n$ is divisible by $a-b$? I know that it is divisible by $a+b $ when $n $ is odd but I want to find out when it is divisible by $a-b$ and when it is not.




number-theory




share|cite













locked by Michael Greinecker♦ yesterday


This question is locked in view of our policy about contest questions. Questions originating from active contests are locked for the duration of the contest, with answers hidden from view by soft-deletion. Please see the comments below for references to the originating contest.














  • For fixed $a,b$ or all $a,b$?
    – lhf
    2 days ago






  • 2




    when $2b^n equiv 0 pmoda-b$, e.g. $a=2b$
    – rtybase
    2 days ago







  • 3




    I'm voting to close this question as off-topic because it is taken from an on going programming competition, codechef.com/AUG18B/problems/GCDMOD
    – lulu
    2 days ago










  • In addition to voting to close this as off-topic, I have flagged it for moderator review, as per the contest problem guidelines.
    – Xander Henderson
    yesterday













up vote
0
down vote

favorite









up vote
0
down vote

favorite











what are the conditions when $a^n+b^n$ is divisible by $a-b$? I know that it is divisible by $a+b $ when $n $ is odd but I want to find out when it is divisible by $a-b$ and when it is not.




number-theory




share|cite













what are the conditions when $a^n+b^n$ is divisible by $a-b$? I know that it is divisible by $a+b $ when $n $ is odd but I want to find out when it is divisible by $a-b$ and when it is not.





number-theory





share|cite












share|cite




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edited 2 days ago









rtybase

8,77221333




8,77221333









asked 2 days ago









Gourav Sharma

72




72




locked by Michael Greinecker♦ yesterday


This question is locked in view of our policy about contest questions. Questions originating from active contests are locked for the duration of the contest, with answers hidden from view by soft-deletion. Please see the comments below for references to the originating contest.






locked by Michael Greinecker♦ yesterday


This question is locked in view of our policy about contest questions. Questions originating from active contests are locked for the duration of the contest, with answers hidden from view by soft-deletion. Please see the comments below for references to the originating contest.













  • For fixed $a,b$ or all $a,b$?
    – lhf
    2 days ago






  • 2




    when $2b^n equiv 0 pmoda-b$, e.g. $a=2b$
    – rtybase
    2 days ago







  • 3




    I'm voting to close this question as off-topic because it is taken from an on going programming competition, codechef.com/AUG18B/problems/GCDMOD
    – lulu
    2 days ago










  • In addition to voting to close this as off-topic, I have flagged it for moderator review, as per the contest problem guidelines.
    – Xander Henderson
    yesterday

















  • For fixed $a,b$ or all $a,b$?
    – lhf
    2 days ago






  • 2




    when $2b^n equiv 0 pmoda-b$, e.g. $a=2b$
    – rtybase
    2 days ago







  • 3




    I'm voting to close this question as off-topic because it is taken from an on going programming competition, codechef.com/AUG18B/problems/GCDMOD
    – lulu
    2 days ago










  • In addition to voting to close this as off-topic, I have flagged it for moderator review, as per the contest problem guidelines.
    – Xander Henderson
    yesterday
















For fixed $a,b$ or all $a,b$?
– lhf
2 days ago




For fixed $a,b$ or all $a,b$?
– lhf
2 days ago




2




2




when $2b^n equiv 0 pmoda-b$, e.g. $a=2b$
– rtybase
2 days ago





when $2b^n equiv 0 pmoda-b$, e.g. $a=2b$
– rtybase
2 days ago





3




3




I'm voting to close this question as off-topic because it is taken from an on going programming competition, codechef.com/AUG18B/problems/GCDMOD
– lulu
2 days ago




I'm voting to close this question as off-topic because it is taken from an on going programming competition, codechef.com/AUG18B/problems/GCDMOD
– lulu
2 days ago












In addition to voting to close this as off-topic, I have flagged it for moderator review, as per the contest problem guidelines.
– Xander Henderson
yesterday





In addition to voting to close this as off-topic, I have flagged it for moderator review, as per the contest problem guidelines.
– Xander Henderson
yesterday
















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