Pregled bibliografske jedinice broj: 1260070
On the D(4)-pairs {;a,ka}; with k ∈ {;2,3,6};
On the D(4)-pairs {;a,ka}; with k ∈ {;2,3,6}; // Glasnik matematički, 58 (2023), 1; 35-57 (međunarodna recenzija, članak, znanstveni)
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Naslov
On the D(4)-pairs {;a,ka}; with k ∈ {;2,3,6};
Autori
Adedji, Kouessi Norbert ; Bliznac Trebješanin, Marija ; Filipin, Alan ; Togbe, Alain
Izvornik
Glasnik matematički (0017-095X) 58
(2023), 1;
35-57
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Diophantine m-tuples ; Pellian equations ; Linear form in logarithms ; Reduction method
Sažetak
Let a and b = ka be positive integers with k ∈ {; ; 2, 3, 6}; ; , such that ab+4 is a perfect square. In this paper, we study the extensibility of the D(4)- pairs {; ; a, ka}; ; . More precisely, we prove that by considering families of positive integers c depending on a, if {; ; 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 4 is a perfect square, then d is given by d = a + b + c + 0.5(abc ±sqrt((ab + 4)(ac + 4)(bc + 4))). As a corollary, we prove that any D(4)- quadruple which contains the pair {; ; a, ka}; ; is regular.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
HRZZ-IP-2018-01-1313 - Diofantska geometrija i primjene (DIOPHANT) (Kazalicki, Matija, HRZZ - 2018-01) ( CroRIS)
Ustanove:
Građevinski fakultet, Zagreb,
Prirodoslovno-matematički fakultet, Split
