Was hoping someone could help with this question - I'd appreciate it.
"Use a direct method of proof to show that if x and y are odd integers, then xy is also odd.
The given solution;
First, notice that if x is odd then x = 2m + 1 where m is an integer. Similarly,
y = 2n + 1 for some integer n. <- I understand up to this point.
Then get lost around here.
Then, xy = (2m + 1)(2n + 1) = 4mn + 2m + 2n + 1 = 2 (2mn + m + n) + 1 which is an odd integer."
Could someone explain what exactly is happening in that section?