JP Journal of Algebra, Number Theory and Applications
Volume 7, Issue 1, Pages 33 - 68
(February 2007)
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ON THE QUADRATIC FORMULA MODULO n
Steve Wright (U. S. A.)
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Abstract: Let a, b, c, and n be integers, with a nonzero and n at least two. Necessary and sufficient conditions on these parameters are derived which guarantee that all solutions of the congruence
are given precisely by the solutions of
where s varies over all solutions of
Corollaries of this result for prime-power moduli are also deduced and some illustrative examples are presented. |
Keywords and phrases: quadratic formula, quadratic residue, quadratic non-residue, congruence modulo n, quadratic congruence. |
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