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Small Solutions of the Congruence ax2 + by2 ≡ c(mod k)

Published online by Cambridge University Press:  20 November 2018

Kenneth S. Williams
Kenneth S. Williams*
Affiliation:
Carleton University
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In 1957, Mordell [3] proved

Theorem. If p is an odd prime there exist non-negative integers x, y ≤ A p3/4 log p, where A is a positive absolute constant, such that

(1.1)

provided (abc, p) = 1.

Recently Smith [5] has obtained a sharp asymptotic formula for the sum where r(n) denotes the number of representations of n as the sum of two squares.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 3 , June 1969 , pp. 311 - 320
Copyright
Copyright © Canadian Mathematical Society 1969

References

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