Can you substitute a = 2n + 1 into a² - 11a + 22?
Let a be an integer. Prove by contraposition that if a^{2} - 11a + 22 is odd then a is even.
Fill in the gaps in the following proof.
Suppose a is odd, so a = 2n + 1 for some integer n.
Then in terms of n, a^{2} - 11a + 22 = 2(..........)
so a^{2} - 11a + 22 is an(.........)
Hence, by contraposition, if a^{2} - 11a + 22 is odd then a is even.