Question

check whether 2^n can end with the digit 6 for any n €N

Answer 1

2^1 (mod 10) = 2

2^2 (mod 10) = 4

2^3 (mod 10) = 8

2^4 (mod 10) = 6

2^5 (mod 10) = 2

It's clear that the units digits of the powers of two repeat in this pattern. Thus, no power of two will have a units digit of 6.