Show that the integral part of `(5+2sqrt(6))^(n)` is odd n is a positive integer .

Show that the integral part of the value of (9+4sqrt5)^n is odd for positive integer .

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

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

Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

Find the least positive integer n such that ((2i)/(1+i))^n is a positive integer.

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

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.

By principle of mathematical induction show that a^(n)-b^(n) is divisible by a+b when n is a positive even 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.