Odd and Even: Difference of Squares (Posted on 2003-04-16)

	Submitted by Gamer
Rating: 3.0000 (4 votes)
Solution:	(Hide)
Express a as (x + y) and b as (x - y) and since a-b is even (odd-odd and even-even are even), in 2y=a-b, y must be an integer. This means x is an integer as well because y, x+y, and x-y are all integers. (x+y)(x-y) expands to (x*x)-(y*y), and since x and y are integers, (x*x) and (y*y) are both perfect squares. The formula is shown in the proof. Since 2y is a-b, just take half of a-b to find y. And since the average of (x+y) and (x-y) is x, use that to find x. So the numbers are ((a+b)/2)² and ((a-b)/2)².

	Subject	Author	Date
	Possible Solution	broll	2023-07-13 23:43:58
	Solution To The Problem	K Sengupta	2007-04-13 23:33:56
	Puzzle Solution	K Sengupta	2007-04-13 23:27:12
	Other uses as well	Gamer	2003-04-16 11:15:51
	re(2): solution	Charlie	2003-04-16 10:18:56
	Solution	Bryan	2003-04-16 08:51:53
	re: solution	jennifer	2003-04-16 08:34:01
	solution	Charlie	2003-04-16 08:29:39
	I think I got it.	jennifer	2003-04-16 08:07:59
	Half of the solution	Hank	2003-04-16 08:02:24