The Fermat equation with polynomial values as base variables.
Previous Page 12
B. Brindza, K. Györy, R. Tijdeman (1985)
Inventiones mathematicae
Hans Peter Schlickewei, Wolfgang M. Schmidt (1995)
Acta Arithmetica
Jan-Hendrik Evertse (1997)
Journal für die reine und angewandte Mathematik
Reese Scott, Robert Styer (2013)
Journal de Théorie des Nombres de Bordeaux
We consider , the number of solutions to the equation in nonnegative integers and integers , for given integers , , , and . When , we show that except for a finite number of cases all of which satisfy for each solution; when , we show that except for three infinite families of exceptional cases. We find several different ways to generate an infinite number of cases giving solutions.
Scott Ahlgren (1999)
Acta Arithmetica
Schlickewei, Hans Peter (1998)
Documenta Mathematica
E. Bombieri, J. Mueller, M. Poe (1997)
Acta Arithmetica
F. Beukers (1991)
Compositio Mathematica
Nir Ailon, Zéev Rudnick (2004)
Acta Arithmetica
Tengely, Szabolcs (2007)
Annales Mathematicae et Informaticae
John Conway, A. Jones (1976)
Acta Arithmetica
W.M. Schmidt, Julia Mueller (1987)
Journal für die reine und angewandte Mathematik
V. Losert (2005)
Acta Arithmetica
Dominik J. Leitner (2011)
Journal de Théorie des Nombres de Bordeaux
The equation , to be solved in non-negative rational integers , has been mentioned by Masser as an example for which there is still no algorithm to solve completely. Despite this, we find here all the solutions. The equation , to be solved in non-negative rational integers and a rational integer , has been mentioned by Corvaja and Zannier as an example for which the number of solutions is not yet known even to be finite. But we find here all the solutions too; there are in fact only six.
Hans Schlickewei (1977)
Acta Arithmetica
Omar Kihel, Florian Luca (2008)
Journal de Théorie des Nombres de Bordeaux
In this paper, we discuss variations on the Brocard-Ramanujan Diophantine equation.
TH. SKOLEM (1955)
Mathematica Scandinavica
M. A. Bennett, M. Filaseta, O. Trifonov (2008)
Acta Arithmetica
B. Brindza (1987)
Compositio Mathematica
Previous Page 12