Question

Prove that 3^2n+7 is divisible by 8​

Answer 1

Explanation:

If n=1 then 32n+7=16=2(8) so true when n=1

Assume true for n=k so

8|32k+7

If n=k+1

32(k+1)+7

32k+2+7

If 32n+7 is divisble by 8 then 32n+7=8A where A∈Z, and thus 32k+2+7=8B where B∈Z

32×32k+7

32×(8A)=72A

72A=8(9A)=9B

So by induction 32n+7 is divisibe by 8 ∀n∈N