15th CanMO 1983 Problem 1 Find all solutions to n! = a! + b! + c! .
We must have n > a, b, c or n!  a, b, c and n > 3, then n! > 3 (n-1)! ≥ a! + b! + c! . So we must have n = 1, 2, or 3. It is easy to check that this gives 3! = 2! + 2! + 2! as the only solution. 15th CanMO 1983 © John Scholes jscholes@kalva.demon.co.uk 21 June 2002