Prove that `5^(25)-3^(25)` id divisible by 2,.

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

Using binomial theorem , Prove that 2^(3n)-7n-1 is divisible by 49.

For any positive integer n, prove that n^(3) - n is divisible by 6.

Prove by induction that if n is a positive integer not divisible by 3. then 3^(2n)+3^(n)+1 is divisible by 13.

Prove by induction that the integer next greater than (3+sqrt(5))^n is divisible by 2^n for all n in N .

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

Prove each of the statements by the principle of mathematical induction : n(n^2 + 5) is divisible by 6, for each natural number n.

Prove the following by using the principle of mathematical induction for all n in N 10^n + 3.4^(n+2) + 5 is divisible by 9.

Prove the statement by the principle of mathematical induction : 3^(2n) - 1 is divisible by 8, for all natural number n.

Prove the following by using the principle of mathematical induction for all n in N 2^(3n) - 1 is divisible by 7.