Prove that `19^(93) - 13 ^(99)` is positive integer divisible by 162.

Prove that ((-1 + isqrt3)/(2))^(3) is a positive integer

Prove by induction that if n is a positive integer not divisible by 3 , then 3^(2n)+3^(n)+1 is divisible by 13 .

Prove that ((-1+isqrt(3))/(2))^(3) is a positive integer.

Find the sum of the first 40 positive integers divisible by 6.

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

Prove that the product of two consecutive positive integers is divisible by 2.

Prove that one of every three consecutive positive integers is divisible by 3.

Prove that one of every three consecutive positive integers is divisible by 3.

Prove that the product of three consecutive positive integers is divisible by 6 .

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