2nd Centromerican 2000 Problem A1 Find all three digit numbers abc (with a ≠ 0) such that a 2 + b 2 + c 2 divides 26.
100, 110, 101, 302, 320, 230, 203, 431, 413, 314, 341, 134, 143, 510, 501, 150, 105 Solution Possible factors are 1, 2, 13, 26. Ignoring order, the possible expressions as a sum of three squares are: 1 = 1 2 + 0 2 + 0 2 , 2 = 1 2 + 1 2 + 0 2 , 13 = 3 2 + 2 2 + 0 2 , 26 = 5 2 + 1 2 + 0 2 = 4 2 + 3 2 + 1 2 . 2nd OMCC 2000 © John Scholes jscholes@kalva.demon.co.uk 30 January 2004 Last corrected/updated 30 Jan 04