Prove that
`1 + w ^( n ) + w ^( 2n) = 3,` if n is multiple of 3
`1 + w ^( n ) + w ^( 2n) = 0,` if n is not multiple of 3 `n in N`

For all n in N , n(n + 1) (n + 5) is a multiple of 8

Prove 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1), AA n in N

If M = {x | x is a multiple of 5} : N = {x | x is a multiple of 7}, then M n N =

N nn W =

Prove that ((2n)!) / (n!) = 2^n(2n - 1) (2n - 3) ... 5.3.1.

Prove that 8^n - 3^n is divisible by 5.

If n is a positive integer not a multiple of 3, then 1+(omega)^n+(omega)^(2n) =

Which of the following sets are equal? : P = {x | x in W, x is a multiple of 2} : Q = {x | x is an even number, x > 1} : R = {x | 2x = n, n in N}

Prove by method of induction: 5^(2n)-2^(2n) is divisible by 3, for all n in N .

Prove by Method of Induction n^3 - 7n + 3 is divisible by 3, AA n in N