Number theory
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Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
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.
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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
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?
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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 $n>0$.
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