If `a > ba n dn` is a positive integer, then prove that `a^n-b^n > n(a b)^((n-1)//2)(a-b)dot`

If n be a positive integer, then prove that (1+i)^n+(1-i)^n=2^(n/2+1)."cos"((npi)/4)

If n is an odd positive integer, then a^(n)+b^(n) is divisible by

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

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

If n is an even positive integer, then a^(n)+b^(n) is divisible by

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

If a and b are distinct integers then prove that (a-b) is a factor of (a^(n)-b^(n)) , whenever n is a positive integar.

If a, b, c are in H.P. and they are distinct and positive then prove that a^n+c^n gt 2b^n