Find all pairs (M,N)of positive integers that satisfy the equation:
M²-MN+2M-3N = 2013

A textbook problem, a textbook solution

Let t=M-N 

Then M=(2013-3t)/(t-1)

One gets M as positive integer   for t= 2, 3,4,6,7,11, 16 and 31;  producing 8 possible couples for  (M,N):   (2007,2005),  (1002,999),  (667,663), (399,393), (332,325,)  (198,187), (131,115), (64,33)

 

   

Edited on May 16, 2015, 4:13 pm

Posted by Ady TZIDON on 2015-05-16 10:35:09