Page **1** of **1**

### BdMO 2017 Dhaka divitional

Posted: **Wed Mar 28, 2018 8:02 pm**

by **soyeb pervez jim**

The $‘energy’$ of an ordered triple $(a,b,c)$ formed by three positive integers $a,b,c$ is said to be $n$, if the following ${a}\leq{b}\leq{c}, gcd(a,b,c)=1$ and $(a^n+b^n+c^n)$ is divisible by $(a+b+c)$. There are some possible ordered triple whose $‘energy’$ can be of all values of ${n}\geq{1}$ In that case, for what is the maximum value of $(a+b+c)$?

### Re: BdMO 2017 Dhaka divitional

Posted: **Fri Mar 30, 2018 11:32 am**

by **samiul_samin**

This problem was posted before in this forum but no solution was given.

### Re: BdMO 2017 Dhaka divitional

Posted: **Sun Feb 10, 2019 3:49 pm**

by **samiul_samin**

soyeb pervez jim wrote: ↑Wed Mar 28, 2018 8:02 pm

The energy of an ordered triple $(a,b,c)$ formed by three positive integers $a,b,c$ is said to be $n$, if the following ${a}\leq{b}\leq{c}, gcd(a,b,c)=1$ and $(a^n+b^n+c^n)$ is divisible by $(a+b+c)$. There are some possible ordered triple whose $‘energy’$ can be of all values of ${n}\geq{1}$ In that case, for what is the maximum value of $(a+b+c)$?

Answer:$3$

Only one solution and $a=b=c=1$