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On the powerful part of n 2 + 1

Jan-Christoph Puchta (2003)

Archivum Mathematicum

We show that n 2 + 1 is powerfull for O ( x 2 / 5 + ϵ ) integers n x at most, thus answering a question of P. Ribenboim.

On two-parametric family of quartic Thue equations

Borka Jadrijević (2005)

Journal de Théorie des Nombres de Bordeaux

We show that for all integers m and n there are no non-trivial solutions of Thue equation x 4 - 2 m n x 3 y + 2 m 2 - n 2 + 1 x 2 y 2 + 2 m n x y 3 + y 4 = 1 , satisfying the additional condition gcd ( x y , m n ) = 1 .

Currently displaying 61 – 80 of 83