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On the unsolvability of some Diophantine equations of a modified Fermat type

Published online by Cambridge University Press:  26 February 2010

K. Inkeri
K. Inkeri
Affiliation:
University of Turku, SF-20500 Turku 50, Finland.
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Extract

In an earlier paper [11] we have discussed the diophantine equation

and the more general equation

when l is an odd prime > 3, c a natural number (or more generally a rational number) satisfying several conditions, n also a natural number and x, y, z, non-zero rational integers. Other investigators have obtained quite a number of results concerning particularly the case n = 1. Obviously, without an essential restriction, we may assume that the natural number c contains no divisor a1n (since such a divisor can be absorbed in the power of z) and furthermore that x, y, z in (1) are relatively prime in pairs.

Type
Research Article
Information
Mathematika , Volume 27 , Issue 2 , December 1980 , pp. 179 - 187
Copyright
Copyright © University College London 1980

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