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The D(−k^2)-triple {;1, k^2 +1, k^2 +4}; with k prime (CROSBI ID 175070)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Filipin, Alan ; Fujita, Yasutsugu
The D(−k^2)-triple {;1, k^2 +1, k^2 +4}; with k prime // Glasnik matematički, 46 (2011), 2; 311-323. doi: 10.3336/gm.46.2.03
Podaci o odgovornosti
Filipin, Alan ; Fujita, Yasutsugu
engleski
The D(−k^2)-triple {;1, k^2 +1, k^2 +4}; with k prime
Let n be a nonzero integer. A set of m distinct 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(-k^2)-triple {; ; 1, k^2 +1, k^2 +4}; ; cannot be extended to a D(-k 2)-quadruple if k >= 5: And if k = 3 we prove that if the set {; ; 1, 10, 13, d}; ; is a D(-9)-quadruple, then d = 45:
Diophantine tuples; simultaneous Diophantine equations
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