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 then prove that (a-b) is a factor of (a^(n)-b^(n)) , whenever n is a positive integar.

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

Solve (x-1)^(n)=x^(n), where n is a positive integer.

If a and b are distinct integers,prove that a^(n)-b^(n) is divisible by (a-b) where n in N

Use factor theorem to prove that (x+a) is a factor of (x^(n)+a^(n)) for any odd positive integer n .

Use factor theorem to verify that x+a is a factor of x^(n)+a^(n) for any odd positive integer.

Use factor theorem to verify that y+a is factor of y^(n)+a^(n) for any odd positive integer n .

Which is not the factor of 4^(6n)-6^(4n) for any positive integer n?

Prove that the function f(x)=x^(n) is continuous at x=n, where 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]