_(3)^(3)^(n)+7quad " is divisible by "8" fon all "n in N

3^(2n)+7 is divisible by 8 for all n varepsilon N

Prove by induction that the sum S_(n)=n^(3)+2n^(2)+5n+3 is divisible by 3 for all n in N.

Prove the following by the principle of mathematical induction: 7^(2n)+2^(3n-3)*3^(n-1) is divisible 25 for all n in N

Using the principle of mathematical induction, prove that (7^(n)-3^(n)) is divisible by 4 for all n in N .

Prove that : 7^(2n)+(2^(3n-3))(3^(n-1)) is divisible by 25 forall n in N .