What is the smallest prime divisor of (5^1999) + (6^1999) ?

a)2 b) 5 c)7 d) 11 e)13

Ok, this sounds like a very simple question. It is. But i am trying out for the maths olympiad tomorrow and I need to know how to do it without relying on the aid of calculating devices. Please help me ( and explain every step if you can).

Jeffreymars16
Mar 13, 2018

#1**+1 **

Here is a START for you.....every power of 5 ends in 5 and every power of 6 ends in 6.....what happens when you add these together....... will it be an odd number? (not divisible by 2) .....it probably won't be divisible by 5 will it? Maybe 7?

What do YOU think???

By looking at the first few terms I see 11 is divisible in the 1st 3rd 5th 7th 9th ....terms

while 2 3 5 7 are not.....I would guess 11.

ElectricPavlov
Mar 13, 2018