Naslov
Bounds for Diophantine quintuples II

Autori
Cipu, Mihai ; Filipin, Alan ; Fujita, Yasutsugu

Izvornik
Publicationes mathematicae (0033-3883) 88 (2016); 59-78

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Diophantine m-tuples ; Pell equations ; linear forms in logarithms ; hypergeometric method

Sažetak
A set of positive integers {; ; ; a1, a2, ..., a_m}; ; ; with the property that a_i*a_j+1 is a perfect square for all distinct indices i and j between 1 and m is called Diophantine m-tuple. In this paper, we show that if {; ; ; a, b, c, d, e}; ; ; is a Diophantine quintuple with a < b < c < d < e and g = gcd(a, b), then b > 3ag ; moreover, if c > a + b + 2\sqrt{; ; ; ab + 1}; ; ; then b > max{; ; ; 24 ag, 2a^1.5g^2}; ; ; . Similar results are given assuming that either ab is odd or c = a + b + 2\sqrt{; ; ; ab + 1}; ; ; .

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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