Even square implies even number

If the square of a number is even, then the number is even.

If you believe…

If a number is not even, then the square of that number is not even.

If you believe…

If a number is odd, then the square of that number is odd.

If you believe…

Any odd number squared equals 2k + 1 for some integer k.

If you believe…

Any odd number squared equals 2(2n2 + 2n) + 1, and let k = 2n2 + 2n.

If you believe…

Any odd number squared equals 4n2 + 4n + 1.

If you believe…

Any odd number equals 2n + 1 for some integer n (by definition).

Advisory

Please note that I am not a mathematician and so the presentation of proofs that I make may be deeply flawed. I'm using this writing process to figure out what I'm reading. Please consult more authoritative sources as well.

Feel free to contact me by leaving a comment or sending me a private message.

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License