20th VMO 1982 Problem A2 Find all real solutions to x(x + 1)(x + 2)(x + 3) = m - 1.
m  25/16, two solutions, x = -3/2 ±√(5/4 + √m) Solution We have m = (x 2 +3x+1) 2 = (x + 3/2) 2 - 5/4. So if m is negative there are no solutions. For non-negative m we have solutions as above Thanks to Suat Namli 19th VMO 1981 © John Scholes jscholes@kalva.demon.co.uk 15 February 2004 Last corrected/updated 15 Feb 04