12th Swedish 1972 Problem 1 Find the largest real number a such that x - 4y = 1, ax + 3y = 1 has an integer solution.
1 Solution For a = 1, we have x = 1, y = 1. Suppose a > 1. Then a(4y+1) = 1-3y, so y = -(a-1)/(4a+3)  -1. Contradiction. So there are no solutions with a > 1. Thanks to Suat Namli 12th Swedish 1972 © John Scholes jscholes@kalva.demon.co.uk 12 February 2004 Last corrected/updated 12 Feb 04