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Small Solutions of the Congruence ax2 + by2 ≡ c(mod k)
Published online by Cambridge University Press: 20 November 2018
Extract
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.
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- Copyright © Canadian Mathematical Society 1969
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