Searching for Diophantine quintuples

• Autorzy: Mihai Cipu , Tim Trudgian
• Języki publikacji: EN

Abstrakty

EN

We consider Diophantine quintuples {a, b, c, d, e}. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $5.441·10^{26}$ Diophantine quintuples.

Kategorie tematyczne

• 11B37: Recurrences
• 11D45: Counting solutions of Diophantine equations
• 11D09: Quadratic and bilinear equations
• 11J86: Linear forms in logarithms; Baker's method

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 4
• Strony: 365-382

Daty

wydano

2016

Twórcy

autor

Mihai Cipu

• Simion Stoilow Institute of Mathematics, of the Romanian Academy, Research unit no. 5, P.O. Box 1-764, RO-014700 Bucureşti, Romania

autor

Tim Trudgian

• Mathematical Sciences Institute, The Australian National University, Canberra, Australia

Identyfikatory

DOI

10.4064/aa8254-2-2016