Hi,

I wanted to clarify my answer for this question. Please note if I did anything wrong.

The question uses induction.

Prove that for every positive integer n, 4^n+14 congruent 0(mod 6)

My work:

P(n): 4^n +14 congruent 0(mod6)

P(1): 4^1 +14 congruent 0(mod6)

18 congruent 0(mod6)

because 6 divides 18-0 since 6*3=18 check!

P(k): 4^k +14 congruent 0(mod6)

4^k +14 divides 6

P(k+1): 4^k +14 + 4^k+1 +14 congruent 0(mod6)


And this is a valid proof.

Am I right? Help is greatly appreciated.