Restate the theorem to prove first before you start the proof. Write all your assumptions before you start the proof. Use the definition of even and/or odd integer. Use the definitions mentioned on page 107, wherever required. Write conclusion once you have proven the given statement.

10. If n is an even integer, 4n12, then n is a sum of two prime numbers.

Definitions on pg. 107:

Common Definitions . Many of the examples in this section and many of the exercises that follow involve elementary number theory, that is, results about integers. It's useful to work in number theory when first starting to construct proofs because many properties of integers, such as what it means to be an even number, are already familiar. The following definitions may be helpful in working some of these exercises. A perfect square is an integer n such that n = k2 for some integer k. A prime number is an integer n >1 such that n is not divisible by any integers other than 1 and n. A composite number n is a nonprime integer; that is, n = ab where a and b are integers with 1 0. For two integers n and m, n divides m, n|m, means that m is divisible by nthat is, m = k(n) for some integer k. The absolute value of a number x,|x|, is x if x = 0 and is - x if x 1 such that n is not divisible by any integers other than 1 and n. A composite number n is a nonprime integer; that is, n = ab where a and b are integers with 1 0. For two integers n and m, n divides m, n|m, means that m is divisible by nthat is, m = k(n) for some integer k. The absolute value of a number x,|x|, is x if x = 0 and is - x if x