Displaying similar documents to “On the Diophantine equation G n ( x ) = G m ( P ( x ) ) for third order linear recurring sequences.”

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...

On subfields of k ( x )

Victor Alexandru, Nicolae Popescu (1986)

Rendiconti del Seminario Matematico della Università di Padova