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.

a and b are positive integers such that a^3 - b^2 is a prime number. Then a^2 - b^2=

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

Write the converse of the following statements. (i) If a number n is even, then n^(2) is even. (ii) If you do all the exercises in the book, you get an A grade in the class. (iii) If two integers a and b are such that a gt b , then a -b is always a positive integer.

The sum of the coefficients in the expansion of (6 x-5 y)^(n) where n is a positive integer, is

Prove binomial theorem for positive integers

a and b are positive integers such that a^(2) - b^(2) is a prime number. Then a^(2) - b^(2) =

Prove that n + n is divisible by 2 for any positive integer n.

State and prove Bionomial theorem for any positive integer n.