Number theory

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Drake
Posts: 1
Joined: Tue Dec 26, 2017 12:00 pm

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: 1007
Joined: Sat Dec 09, 2017 1:32 pm

Re: Number theory

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

NABILA
Posts: 28
Joined: Sat Dec 15, 2018 5:19 pm
Location: Munshigonj, Dhaka

Re: Number theory

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