31st Swedish 1991 Problem 1 Find all positive integers m, n such that 1/m + 1/n - 1/(mn) = 2/5.
(m,n) = (3,10), (4,5), (5,4) or (10,3) Solution We have (2m-5)(2n-5) = 15, so {2m-5,2n-5} = {1,15} or {3,5} Thanks to Suat Namli 31st Swedish 1991 © John Scholes jscholes@kalva.demon.co.uk 16 January 2004 Last corrected/updated 16 Jan 04