Electronic Proceedings of the Twenty-third Annual International Conference on Technology in Collegiate Mathematics

Denver, Colorado, March 17-20, 2011

Paper C009

This is an electronic reprint, reproduced by permission of Pearson Education Inc. Originally appeared in the Proceedings of the Twenty-third Annual International Conference on Technology in Collegiate Mathematics, ISBN 0-321-68984-4, Copyright (C) 2012 by Pearson Education, Inc.


Solving Cubic Congruences Modulo A Prime On The TI -89

Joseph Fadyn


Southern Polytechnic State University

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ABSTRACT

The author presents a technique which implements Cardano’s classical method to solve the cubic congruence: Ax3 + Bx2 + Cx+D 0 (modulo p) where p is a prime. Discussion centers around the components needed to apply Cardano’s method in this situation: modular exponentiation, modular inverses and finding square roots and cube roots modulo a prime p.

Keyword(s): number theory, TI-89