Proof

a.

Prove that $3n + 1)^2 - (3n - 1)^2$ is always a multiple of 12, for all positive integer values of $n$ .

[2]

b.

Hence prove that $3n + 1)^4 - (3n - 1)^4$ is always a multiple of 24, for all positive integer values of $n$ .

[2]

Proof

a.

Prove that $3n + 1)^2 - (3n - 1)^2$ is always a multiple of 12, for all positive integer values of $n$ .

[2]

b.

Hence prove that $3n + 1)^4 - (3n - 1)^4$ is always a multiple of 24, for all positive integer values of $n$ .

[2]

Proof

Proof Questions