proof by contrapositive help

Let *a* be an integer. Prove by contraposition that if *a*^{2} - 11*a* + 22 is odd then *a* is even.

Fill in the gaps in the following proof.

Suppose *a* is odd, so *a* = 2*n* + 1 for some integer *n*.

Then in terms of *n*, *a*^{2} - 11*a* + 22 = 2(..........)

so *a*^{2} - 11*a* + 22 is an(.........)

Hence, by contraposition, if *a*^{2} - 11*a* + 22 is odd then *a* is even.

Re: proof by contrapositive help

Can you substitute a = 2n + 1 into a² - 11a + 22?

Re: proof by contrapositive help

thats what I was thinking, but am gona ask my teacher who wrote this, cause I dont understand what to do

and what is 2 being factored out of ?

Re: proof by contrapositive help

Quote:

Originally Posted by

**Tweety** and what is 2 being factored out of ?

2 is being factored out of the result of substitution of 2n + 1 for *a* in *a*² - 11*a* + 22. To do the substitution, replace *a* in *a*² - 11*a* + 22 with 2n + 1 and perform the simplification.