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Sharper ABC-based bounds for congruent polynomials

Daniel J. Bernstein — 2005

Journal de Théorie des Nombres de Bordeaux

Agrawal, Kayal, and Saxena recently introduced a new method of proving that an integer is prime. The speed of the Agrawal-Kayal-Saxena method depends on proven lower bounds for the size of the multiplicative semigroup generated by several polynomials modulo another polynomial $h$ . Voloch pointed out an application of the Stothers-Mason ABC theorem in this context: under mild assumptions, distinct polynomials $A, B, C$ of degree at most $1.2 deg h - 0.2 deg rad A B C$ cannot all be congruent modulo $h$ . This paper presents two improvements...

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