If you could check my 2 proofs and help me start on one please.

1a) If is a multiple of 2, then is a multiple of 2. Domain of n is all integers.

My proof:

An integer n is even if there exists an integer k such that n = 2k.

n = 2k,

is an integer therefore is even, thus making it a multiple of 2.

By the definition of n = 2k, n is also a multiple of 2.

1b) is an irrational number.

My proof(by contradiction):

is a positive number such that its cube is 2.

Assume is rational.

integers P, Q such that = , fully simplified.

(Corollary: If is even, then n is even. (proven in 1a))

An integer n is even if there exists an integer k such that n = 2k.

is an integer, therefore Q is even, along with P.

Since P and Q are even, they share a common factor. Since we defined that was fully simplified, we have a contradiction.

Now the one I am having a hard time with is

2) Prove or disprove the following proposition: If x and y are positive integers such that x > y + 1, then is not prime.

Thanks in advance

James