prove this certainty?

Question

prove without using Fermats last theorem that it is imposible to write
(5a)^(n) + (5a + 2)^(n) = (v)^(n)
for natural solutions of "a" & "v" having n>1.

Answer 1

suppose a is even say 2k then
2^n(5k)^n + 2^n(5k+1)^n = v^n
then 2 divides v,

So we can assume that a is odd ( because if it is not you can divide 2 out and still have a solution )

the rest is easy yopu va=can do that by yourself

Answer 2

It should be true for a certain n, you can determine, then if you assume it for a n it is possible to implement for the next n and then it is done

Answer 3

Try to prove by induction, then show that it cannot be (it might lead to contradiction)