On the size of Diophantine m-tuples in imaginary quadratic number rings (CROSBI ID 294108)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Adžaga, Nikola
engleski
On the size of Diophantine m-tuples in imaginary quadratic number rings
A Diophantine m-tuple is a set of m distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers. We study the same problem in the rings of integers of imaginary quadratic fields. By using a gap principle proven by Diophantine approximations, we show that m≤42. Our proof is relatively simple compared to the proofs of similar results in positive integers.
Diophantine m-tuples ; Diophantine approximation ; Pell equations ; rings of integers ; Diophantine equations
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Podaci o izdanju
11 (1)
2021.
1950020
10
objavljeno
1664-3607
1664-3615
10.1142/S1664360719500206