3²ⁿ +7 is divisible by 8 for all n E N

Let P(n)  be the statement that  3²ⁿ + 7 is divisible by 8 for all n belongs to N 

So P(1) = 16 , which is divisible by 8

Let P(k) be true , hence 3^2k + 7 is divisible by 8  , which means 3^2k + 7 = 8m , here m is a natural number (1)

So P(k + 1) = 3^2(k+1) + 7 = 3^2k .3² + 7 
= 9.3^2k + 7
= 9(3^2k  +7 ) - 56
= 9.(8m) - 56  [from (1) ]
As both the terms are divisible by 8 , hence P(k+1) is also true .

So P(n) is true .