36th BMO 2000 Problem 3 Find positive integers m, n such that (m 1/3 + n 1/3 - 1) 2 = 49 + 20 (6 1/3 ).
A little experimentation gives (2·6 1/3 + 2·6 2/3 - 1) 2 = 49 + 20·6 1/3 . So we can take m = 48, n = 288. 36th BMO 2000 © John Scholes jscholes@kalva.demon.co.uk 18 Jul 2002