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On recursive solutions of a unit fraction equation

Published online by Cambridge University Press:  09 April 2009

Lawrence Brenton
Affiliation:
Wayne State University, Detroit, Michigan 48202, U.S.A., [email protected]
Robert R. Bruner
Affiliation:
Wayne State University, Detroit, Michigan 48202, U.S.A., [email protected]
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Abstract

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We 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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

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