The pairs of positive integers (A, B) are such that B divides 2A².

Prove that A² + B cannot be a perfect square.

 

....................I 've   erroneously solved the case that A^2 DIVIDES  B

and proved the oppposite- then edited by adding this remark...........................................................

 Text  prior to my edit:

LET B/2A^2=K

 

A^2+B=A^2*(2K+1)  =(SAY ) N

 FOR  N TO BE A SQUARE OF INTEGER   (2K+1) MUST  BE A SQUARE OF INTEGER,WHICH IS   POSSIBLE  , for if

b=32  and A=2        k=4         k*2+1=9

 

and 32+4 is a square

..................Now i am going to solve the original -hopefully

 

 

 

 

Edited on May 7, 2008, 11:31 am

Posted by Ady TZIDON on 2008-05-07 11:14:10