✔ 最佳答案
There are little problems.
First, how do you infer that "xy = (2k + 1)^2" from "xy = 2k + 1"?
Second, how do you infer that "but xy is even" from "xy = 4q + 1"?
You may prove it like this instead:
Let x be odd (2k + 1) and y be even (2p), where k and p are integers.
xy = (2k + 1)(2p)
xy = 2[p(2k + 1)]
Thus, xy is even.
Edit:
You don't prove it indirectly.
If you assume xy is odd, you assume
xy = 2k + 1 where k is an integer.
But if you define xy as 2k + 1, you already agree that
2k is even whether k is even or odd, implying that
2k is even even k is odd.
There is no need to assume xy is odd while confirming unconsciously that 2k is even.
