Glasnik matematički, Vol. 46 No. 2, 2011.
Original scientific paper
https://doi.org/10.3336/gm.46.2.03
The D(-k2)-triple {1,k2+1,k2+4} with k prime
Alan Filipin
; Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića-Miošića 26, 10 000 Zagreb, Croatia
Yasutsugu Fujita
; Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan
Abstract
Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the product of any two of them increased by n is a perfect square. Let k be a prime number. In this paper we prove that the D(-k2)-triple {1,k2+1,k2+4} cannot be extended to a D(-k2)-quadruple if k≠3. And for k=3 we prove that if the set {1,10,13,d} is a D(-9)-quadruple, then d=45.
Keywords
Diophantine tuples; simultaneous Diophantine equations
Hrčak ID:
74261
URI
Publication date:
23.11.2011.
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