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On the Equations xn±yn = zm

Published online by Cambridge University Press:  03 November 2016

R. G. Beerensson
R. G. Beerensson*
Affiliation:
10 Muirfield, Perth, Scotland
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Extract

1. We determine first an infinity of solutions of the equation xn-yn=zm when m, n are relatively prime. Let p be an odd prime; then q= pm has a primitive root g, say, and so, if ϕ is Euler's function, x= gϕ(q) satisfies xn= gnϕ(q)) = l (mod q).

Type
Research Article
Information
The Mathematical Gazette , Volume 54 , Issue 388 , May 1970 , pp. 138 - 139
Copyright
Copyright © Mathematical Association 1970

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