Vol. 50, No. 2, 1974

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ISSN: 0030-8730
On a problem of Hurwitz

Norman Peter Herzberg

Vol. 50 (1974), No. 2, 485–493
Abstract

A. Hurwitz proposed the problem of finding all the positive integers z,x = (x1,,xn) satisfying the diophantine equation x12 + + xn2 = z x1,,xn. This paper investigates the question of which values of z can occur, using only the most elementary techniques. An algorithm is given for determining all permissible values of (z,n) for all n below a given bound. As an application it is established that the only possible values in the range z (n + 15)4 are z = n,z = (n + 8)3 when n is odd, and z = (n + 15)4. As another application the fifteen values of n 131,020 for which the only permissible value of z is n have been found.

Mathematical Subject Classification
Primary: 10B20
Secondary: 10B05
Milestones
Received: 11 October 1972
Published: 1 February 1974
Authors
Norman Peter Herzberg