J Austral Math Soc Ser A 57 pp341--356, 1994.

On Recursive Solutions of a Unit Fraction Equation

Lawrence Brenton and Robert R. Bruner

(Received 24 October 1990; revised 10 March 1992)

Abstract

We consider the Egyptian fraction equation 1 = å^N_i=1 1/n_i + 1/(Õ^N_i=1 n_i) and discuss techniques for generating solutions. By examining a quadratic recurrence relation modulo a family of primes we have found some 500 new infinite sequences of solutions. We also initiate an investigation of the randomness of the distribution of solutions, and sho that there are infinitely many solutions not generated by thee aforementioned technique.

1991 AMS Subject Classification: 11D68, 11N45, 11B50, 11Y50

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Authors

Lawrence Brenton: Wayne State University, Detroit, Michigan 48202, U.S.A.
mailto:brenton@math.wayne.edu
Robert R. Bruner: Wayne State University, Detroit, Michigan 48202, U.S.A.
mailto:rrb@math.wayne.edu

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Last Modified: Thu Jan 9 9:04:22 2003