12th Australian 1991 Problem A2 Find all positive integers n which divide the least common multiple of 1, 2, 3, ... , n-1.
all n not a prime or prime power Solution A prime or prime power obviously does not work. Suppose n is not a prime or prime power. Then if p k divides n, we have p k < n and hence p k divides the lcm. Thanks to Suat Namli Solutions are also available in Australian Mathematical Olympiads 1979-1995 by H Lausch and P J Taylor, ISBN 0858896451, published by Australian Mathematics Trust. It can be ordered from AMT by email. 12th Aus 1991 © John Scholes jscholes@kalva.demon.co.uk 5 February 2004 Last corrected/updated 5 Feb 04