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### Number theory

Posted: Tue Dec 26, 2017 12:13 pm
The energy of an ordered triple(a,b,c) formed by 3 positive integers a,b,c is said to be n and a<=b<=c and GCD(a,b,c)=1. There are some possible triples for which a^n+b^n+c^n is divisible by a+b+c for all n>0. Find the maximum possible value of a+b+c.

### Re: Number theory

Posted: Sat Mar 03, 2018 9:53 pm
I'll Latex it for you:
The energy of a ordered triple ($a,b,c$) formed by $3$ positive integers $a,b,c$ is said to be $n$ and $a\leq b\leq c$ & GCD($a,b,c$)$=1$.There are some possible triples for $a^n+b^n+c^n$ is divisible by $a+b+c$ for all $n>0$.Find the maximum possible value of $a+b+c$.

Note

### Re: Number theory

Posted: Wed Jan 16, 2019 1:07 pm
samiul_samin wrote:
Sat Mar 03, 2018 9:53 pm
There are some possible triples for $a^n+b^n+c^n$ is divisible by $a+b+c$ for all $n>0$.
@Drake
Are you sure about this?   ### Re: Number theory

Posted: Sun Feb 10, 2019 3:52 pm
NABILA wrote:
Wed Jan 16, 2019 1:07 pm
samiul_samin wrote:
Sat Mar 03, 2018 9:53 pm
There are some possible triples for $a^n+b^n+c^n$ is divisible by $a+b+c$ for all $n>0$.
@Drake
Are you sure about this?   This is from dhaka regional 2017.