Using Binomial Theorem, show that `6^n - 5n - 1` is divisible by 25, where n is any natural number.

n^2-1 is divisible by 8, if n is

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

Show that n^7-n is divisible by 42 .

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

Use Binomial Theorem to find : (51)^6 .

Use Binomial Theorem to find : (98)^5 .

Use the principle of mathematical induction to show that a^(n) - b^n) is divisble by a-b for all natural numbers n.

Use Binomial Theorem to find : (999)^5 .