ON RECURSIVE SOLUTIONS OF A UNIT FRACTION EQUATION

Authors
BRENTON L BRUNER RR
Citation
L. Brenton et Rr. Bruner, ON RECURSIVE SOLUTIONS OF A UNIT FRACTION EQUATION, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 57, 1994, pp. 341-356
Citations number
11
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics → ACNP
ISSN journal
02636115
Volume
57
Year of publication
1994
Part
3
Pages
341 - 356
Database
ISI
SICI code
0263-6115(1994)57:<341:ORSOAU>2.0.ZU;2-Y
Abstract
We consider the Egyptian fraction equation 1 = SIGMA(i=1)N 1/n(i) + 1/ (PI(i=1)N n(i)) and discuss techniques for generating solutions. By ex amining a quadratic recurrence relation modulo a family of primes we h ave found some 500 new infinite sequences of solutions. We also initia te an investigation of the randomness of the distribution of solutions , and show that there are infinitely many solutions not generated by t he aforementioned technique.