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

n^7-n is divisible by 42 .

3^(2n+2)-8n-9 is divisible by 8.

Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,...

n^2 -1 is divisible by 8, if n is

For every positive integer n, prove that 7^(n) – 3^(n) is divisible by 4.

Statement -1 for all natural numbers n , 2.7^(n)+3.5^(n)-5 is divisible by 24. Statement -2 if f(x) is divisible by x, then f(x+1)-f(x) is divisible by x+1,forall x in N .

Prove that n^(2)-n is divisible by 2 for every positive integer n.

Prove that n + n is divisible by 2 for any positive integer n.

Prove that 3^(2n)+24n-1 is divisible by 32 .

10^n+3(4^(n+2))+5 is divisible by (n in N)