Using principle of MI prove that `2.7^n+3.5^n-5` is divisible by 24

Prove that 2.7^(n)+3.5^(n)-5 is divisible by 24, for all n in N

Using binomial theorem,prove that 2^(3n)-7^(n)-1 is divisible by 49, where n in N

Using binomial theorem, prove that (2^(3n)-7n-1) is divisible by 49, where n in N.

Prove the following by the principle of mathematical induction: 5^(n)-1 is divisible by 24 for all n in N.

Using binomial theorem,prove that 3^(2n+2)-8^(n)-9 is divisible by 64, where n in N.

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

5^(2n+2)-24n+25 is divisible by 576

Prove the following by the principle of mathematical induction: 2.7^(n)+3.5^(n)-5 is divisible 25 for all n in N