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The extendibility of Diophantine pairs I : the general case (CROSBI ID 195338)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Filipin, Alan ; Fujita, Yasutsugu ; Togbe, Alain
The extendibility of Diophantine pairs I : the general case // Glasnik matematički, 49 (2014), 1; 25-36. doi: 10.3336/gm.49.1.03
Podaci o odgovornosti
Filipin, Alan ; Fujita, Yasutsugu ; Togbe, Alain
engleski
The extendibility of Diophantine pairs I : the general case
Let $a$ and $b$ be positive integers with $a < b$, such that $ab+1$ is a perfect square. In this paper we give an upper bound for the minimal positive integer $c$ such that ${; ; ; a, b, c, d}; ; ; $ is the set of positive integers which has the property that the product of any two of its elements increased by $1$ is a perfect square and $d\neq a+b+c+2(abc\pm\sqrt{; ; ; (ab+1)(ac+1)(bc+1)}; ; ; )$.
Diophantine tuples ; simultaneous Diophantine equations
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