Perfect Square Not (Posted on 2008-05-07)

	Submitted by K Sengupta
Rating: 2.0000 (3 votes)
Solution:	(Hide)
At the outset, we substitute 2A2 = c*B. Since B divides 2A2, it follows that c must be a positive integer. If possible, let us suppose that: A2 + B = G2, for some positive integer G Then, we have: A2*c2 + B*c2 = G2*c2 or, A2*c2 + 2A2*c = G2*c2 or, A2(c2 + 2c) = (G*c)2......(*) But, c2 < c2 + 2c < (c+1)2, and accordingly, the lhs of (*) cannot be the square of a positive integer. This leads to a contradiction. Consequently, A2 + B cannot be a perfect square. *************************************** For an alternative methodology, refer to the solution submitted by Praneeth in this location.

	Subject	Author	Date
	re: Solution	K Sengupta	2008-05-26 14:13:59
	Another solution	Jonathan Lindgren	2008-05-24 15:52:32
	Solution	Praneeth	2008-05-09 04:00:07
	re: To B not a square >>>. Revisited	Ady TZIDON	2008-05-07 19:15:48
	To B not a square	Gamer	2008-05-07 17:22:09
	NO WAY	Ady TZIDON	2008-05-07 11:14:10