### Sharper ABC-based bounds for congruent polynomials

Daniel J. Bernstein (2005)

Journal de Théorie des Nombres de Bordeaux

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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 $1.2degh-0.2degradABC$ cannot all be congruent modulo $h$. This paper presents two...