Prove using the Principle of Induction.
5^(2n)-4^n is divisible by 7 for any positive integer n.
For n=1 we have
5^2-4^1=25-4=21=3*7. So divisible by 7.
Suppose the property is true for n=k, ...
Using the Principle of Induction to prove that some expression depending on integer number n is divisible by 7 for every positive integer n.