## Number theory

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### Number theory

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.

- samiul_samin
**Posts:**999**Joined:**Sat Dec 09, 2017 1:32 pm

### Re: Number theory

I'll

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 $a+b+c$.

**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

@Drakesamiul_samin wrote: ↑Sat Mar 03, 2018 9:53 pmThere are some possible triples for $a^n+b^n+c^n$ is divisible by $a+b+c$ for all $n>0$.

Are you sure about this?

Wãlkîñg, lõvǐñg, $mīlïñg @nd lìvíñg thě Lîfè

- samiul_samin
**Posts:**999**Joined:**Sat Dec 09, 2017 1:32 pm

### Re: Number theory

This is from dhaka regional 2017.NABILA wrote: ↑Wed Jan 16, 2019 1:07 pm@Drakesamiul_samin wrote: ↑Sat Mar 03, 2018 9:53 pmThere are some possible triples for $a^n+b^n+c^n$ is divisible by $a+b+c$ for all $n>0$.

Are you sure about this?

Answer