a.) Prove the following theorem:
If k is the square of an integer that is even, then k is the sum of 2 successive odd integers.
b.) State the converse of the theorem. If it's true, prove it. If it's false, give a counterexample.
For a.), I'm not quite sure how to prove it, but I looked at what it means, that is, I know
2^2 = 1 + 3
4^2 = 7 + 9
6^2 = 17 + 19
8^2 = 31 + 33
etc.. I kind of see a pattern
For b.), the converse would be "If k is the sum of 2 successive odd integers, then k is the square of an even integer"
This is false. Example: 12 = 5 + 7, but 12 is not the square of an even integer.