BdMO Online Forum

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.

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

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?

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.
Answer