Glasnik matematički, Vol. 45 No. 1, 2010.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.45.1.02
The number of Diophantine quintuples
Yasutsugu Fujita
; Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan
Sažetak
A set {a1, ... ,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is a perfect square for all i, j with 1 ≤ i < j ≤ m. It is known that there does not exist a Diophantine sextuple and that there exist only finitely many Diophantine quintuples. In this paper, we first show that for a fixed Diophantine triple {a,b,c} with a < b < c, the number of Diophantine quintuples {a,b,c,d,e} with c < d < e is at most four. Using this result, we further show that the number of Diophantine quintuples is less than 10276, which improves the bound 101930 due to Dujella.
Ključne riječi
Simultaneous Diophantine equations; Diophantine tuples
Hrčak ID:
52364
URI
Datum izdavanja:
17.5.2010.
Posjeta: 964 *