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On a family of two-parametric D(4)-triples

Alan Filipin ; Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića-Miošića 26, 10000 Zagreb, Croatia
Bo He ; Department of Mathematics, ABa Teacher's College, Wenchuan, Sichuan, 623000, P. R. China
Alain Togbé   ORCID icon ; Mathematics Department, Purdue University North Central, 1401 S, U.S. 421, Westville IN 46391, USA

Puni tekst: engleski, pdf (189 KB) str. 31-51 preuzimanja: 242* citiraj
APA 6th Edition
Filipin, A., He, B. i Togbé, A. (2012). On a family of two-parametric D(4)-triples. Glasnik matematički, 47 (1), 31-51.
MLA 8th Edition
Filipin, Alan, et al. "On a family of two-parametric D(4)-triples." Glasnik matematički, vol. 47, br. 1, 2012, str. 31-51. Citirano 07.12.2021.
Chicago 17th Edition
Filipin, Alan, Bo He i Alain Togbé. "On a family of two-parametric D(4)-triples." Glasnik matematički 47, br. 1 (2012): 31-51.
Filipin, A., He, B., i Togbé, A. (2012). 'On a family of two-parametric D(4)-triples', Glasnik matematički, 47(1), str. 31-51.
Filipin A, He B, Togbé A. On a family of two-parametric D(4)-triples. Glasnik matematički [Internet]. 2012 [pristupljeno 07.12.2021.];47(1):31-51.
A. Filipin, B. He i A. Togbé, "On a family of two-parametric D(4)-triples", Glasnik matematički, vol.47, br. 1, str. 31-51, 2012. [Online].

Let k be a positive integer. In this paper, we study a parametric family of the sets of integers {k,A2k+4A,(A+1)2k+4(A+1),d}. We prove that if d is a positive integer such that the product of any two distinct elements of that set increased by 4 is a perfect square, then
d= (A4 + 2A3 + A2)k3 + (8A3 + 12A2 + 4A)k2 + (20A2 + 20A + 4) k + (16A + 8)
for 1≤ A ≤22 and A ≥ 51767.

Ključne riječi
Diophantine m-tuples; Pell equations; Baker's method

Hrčak ID: 82569


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