If a and b are distinct integers, prove that a-b is a factor of `a^n` - `b^n` , whenever n is a positive integer.

If aa n db are distinct integers, prove that a-b is a factor of a^n-b^n , wherever n is a positive integer.

If a and b are distinct integers,Using Mathematical Induction prove that a - b is a factor of a^n-b^n , whenever n is a positive integer.

If n is an odd integer, prove that n^(2) is also an odd integer.

Prove that the function f(x)= x^(n) is continuous at x= n, where n is a positive integer.

If n is an odd integer, Prove that 16 is a divisor of n^4 + 4n^2 + 11 .

Show that 9^(n+1)-8n-9 is divisible by 64, where n is a positive integer.

By induction method prove that, (a^(n)+b^(n)) is divisible by (a+b) when n is an odd positive integer .

If n is a positive integer then .^(n)P_(n) =

Using permutation or otherwise, prove that (n^2)!/(n!)^n is an integer, where n is a positive integer. (JEE-2004]

Prove that 2^(n) gt n for all positive integers n.