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

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

Prove that 7^(n) - 6n - 1 is always divisible by 36.

Using principle of mathematical induction, prove that 7^(4^(n)) -1 is divisible by 2^(2n+3) for any natural number n.

If ninN,10^(2n-1)+1 is divisible by

Show that 5^(2n) -1 is divisible for all n in N by 24.

If p is a fixed positive integer, prove by induction that p^(n +1) + (p + 1)^(2n - 1) is divisible by P^2+ p +1 for all n in N .

Prove that ((n + 1)/(2))^(n) gt n!

Use induction to prove that n^(3) - n + 3 , is divisible by 3, for all natural numbers n