Hi,

I'm trying to show that 4*6^(2n) + 3*2^(3n) is divisible by 7 for any positive integer n.

This works for n = 1. I then suppose it holds for n = k, and subsequently try to manipulate n = k+1 to have factors 7 and n = k, but I don't seem to get anywhere.

For n = k we have

4*6^(2k) + 3*2^(3k)

Assume this is divisible by 7. Then for n = k + 1 we have

4*6^(2(k+1)) + 3*2^(3(k+1)

= 4*6^(2k+2) + 3*2^(3k+3)

= 4*36*6^(2k) + 3*8*2^(3k)

This is as far as I get I'm afraid Any help at all would be much appreciated