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A NOTE ON SIMULTANEOUS CONGRUENCES, II: MORDELL REVISED

Part of: Diophantine equations

Published online by Cambridge University Press:  25 March 2010

TREVOR D. WOOLEY
TREVOR D. WOOLEY*
Affiliation:
School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, UK (email: [email protected], [email protected])
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Abstract

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When p is a prime number, and k1,…,kt are natural numbers with 1≤k1<k2<⋯<kt<p, we show that the simultaneous congruences ∑ t1xkji≡∑ t1ykjimod p (1≤j≤t) possess at most k1⋯ktpt solutions with 1≤xi,yi≤p (1≤i≤t). Analogous conclusions are provided when one or more of the exponents ki is negative.

Keywords

congruences in many variablesexponential sums

MSC classification

Secondary: 11D79: Congruences in many variables
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 2 , April 2010 , pp. 261 - 275
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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