4th Swedish 1964 Problem 2 Find all positive integers m, n such that n + (n+1) + (n+2) + ... + (n+m) = 1000.
(m,n) = (15,55), (24,28), (4,198). Solution There are m+1 terms, average size (2n+m)/2. So (m+1)(2n+m) = 2000 = 16·125. Note that m+1 and 2n+m have opposite parity. Also 1 < m+1 < 2n+m. So we have m+1 = 16, 25 or 5. 4th Swedish 1964 © John Scholes jscholes@kalva.demon.co.uk 30 December 2003 Last corrected/updated 30 Dec 03