Question

how to solve these type of question as present in the picture

Answer 1

n is all position integer as given.
so fist we put n=1
as 7^1-3^1=4 means it is divisible by 4
then we put n=k
as 7^k-3^k=4d we supposing that it is divisible by 4
then we put n= k+1
as 7^k+1-3^k+1
we add and subtract 7.3k
and solve it