Vol. 40, No. 1, 1972

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The Diophantine equation u(u + 1)(u + 2)(u + 3) = v(v + 1)(v + 2)

David W. Boyd and Hershy Kisilevsky

Vol. 40 (1972), No. 1, 23–32
Abstract

In this paper we demonstrate that the equation of the title has exactly three solutions in positive integers, namely: 1 2 3 4 = 2 3 4,2 3 4 5 = 4 5 6 and 19 20 21 22 = 55 56 57. The method of proof is to reduce the equation to the form y2 = x3 x + 1.

Mathematical Subject Classification
Primary: 10B10
Milestones
Received: 11 May 1970
Published: 1 January 1972
Authors
David W. Boyd
Department of Mathematics
University of British Columbia
Vancouver BC V6T 1Z2
Canada
http://www.math.ubc.ca/~boyd/boyd.html
Hershy Kisilevsky
Department of Mathematics and Statistics
Concordia University
1455 de Maisonneuve Blvd West
Montreal H3G1M8
Canada