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.

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

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

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

Find the sum of : the first n positive integers

if A =[(3,-4),( 1,-1)] then prove that A^n = [ ( 1+2n, -4n),( n,1-2n)] where n is any positive integer .

if A =[(3,-4),( 1,-1)] then prove that A^n = [ ( 1+2n, -4n),( n,1-2n)] where n is any positive integer .

Using contrapositive method prove that if n^(2) is an even integer, then n is also an even integers.

If A is a square matrix and |A| = 2 then |A|^n = ………. . Where n is positive integer.

Write the converse of the following statements: If two integers a and b are such that agtb , then a-b is always a positive integer.

If a, b, c, d are distinct integers in A. P. Such that d=a^2+b^2+c^2 , then a + b + c + d is