On recursive solutions of a unit fraction equation-Reference-Cited by-同舟云学术

On recursive solutions of a unit fraction equation

Published:1994-12 Issue:3 Volume:57 Page:341-356
ISSN:0263-6115
Container-title:Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
language:en
Short-container-title:J Aust Math Soc A

Author:

Brenton Lawrence,Bruner Robert R.

Abstract

AbstractWe consider the Egyptian fraction equation 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 show that there are infinitely many solutions not generated by the aforementioned technique.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics,Statistics and Probability

Reference10 articles.

1. On Kellogg's Diophantine Problem

2. On the Diophantine equation 1 =∑1∕ni+ 1∕∏niand a class of homologically trivial complex surface singularities

3. On stambrøker;Johannessen;Nord. Mat. Tidskr.,1974

4. On a Point in the Theory of Vulgar Fractions

5. On distinct unit fractions whose sum equals 1

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