Number theory

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
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.
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: 999
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: 23
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
Are you sure about this?   Wãlkîñg, lõvǐñg, $mīlïñg @nd lìvíñg thě Lîfè samiul_samin Posts: 999 Joined: Sat Dec 09, 2017 1:32 pm Re: Number theory NABILA wrote: Wed Jan 16, 2019 1:07 pm samiul_samin wrote: Sat Mar 03, 2018 9:53 pm There are some possible triples for$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.