24th Swedish 1984 Problem 5 Find all positive integer solutions to a 3 - b 3 - c 3 = 3abc, a 2 = 2(a + b + c).
(a,b,c) = (4,1,3), (4,2,2), (4,3,1) Solution The first equation shows that a > b and c. So the second equation gives a 2  0. 24th Swedish 1984 © John Scholes jscholes@kalva.demon.co.uk 27 February 2004 Last corrected/updated 3 Mar 04