Show that there is no integer 'a' such that `a^2-3a-19` is divisible by 289.

If n is a positive integer, show that: 4^n-3n-1 is divisible by 9

If n is an odd positive integer, show that (n^2-1) is divisible by 8.

If n is an odd positive integer, show that (n^2-1) is divisible by 8.

If n is a positive integer, show that 4^n -3n -1 is divisible by 9

Prove that 33! is divisible by " 2^15 . what is the largest integer n such that 33! is divisible by 2^n .

If n is positive integer show that 9^n+7 is divisible 8

Prove that 33! Is divisible by 2^(19) and what is the largest integer n such that 33! Is divisible by 2^(n) ?

Show that : 15^(3) - 8^(3) is divisible by 7

If n is a positive integer, then show that 6^(n)-5n-1 is divisible by 25

Show that : 15^(3) + 8^(3) is divisible by 23.