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001-es BibID:	BIBFORM103953
035-os BibID:	(WOS)000567437900022 (Scopus)85087218222
Első szerző:	Tengely Szabolcs (matematikus)
Cím:	On a Diophantine equation of Erdős and Graham / Szabolcs Tengely, Maciej Ulas, Jakub Zygado
Dátum:	2020
ISSN:	0022-314X 1096-1658
Megjegyzések:	We study solvability of the Diophantine equation n/2(n) = Sigma(k)(i=1) a(i)/2(ai), in integers n, k, a(1), ..., a(k) satisfying the conditions k >= 2 and a(i) < a(i+1 )for i = 1, ..., k - 1. The above Diophantine equation (of polynomial-exponential type) was mentioned in the monograph of Eras and Graham, where several questions were stated. Some of these questions were already answered by Borwein and Loring. We extend their work and investigate other aspects of Erdos and Graham equation. First of all, we obtain the upper bound for the value a(k) given in terms of k only. This mean, that with fixed k our equation has only finitely many solutions in n, a(1), ..., a(k). Moreover, we construct an infinite set K, such that for each k is an element of K, the considered equation has at least five solutions. As an application of our findings we enumerate all solutions of the equation for k <= 8. Moreover, by applying greedy algorithm, we extend Borwein and Loring calculations and check that for each n <= 10(4) there is a value of k such that the considered equation has a solution in integers n + 1 = a(1) < a(2) < ... < a(k). Based on our numerical calculations we formulate some further questions and conjectures.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk Erdős and Graham equation Polynomial exponential Diophantine equation Sum of fractions
Megjelenés:	Journal of Number Theory. - 217 (2020), p. 445-459. -
További szerzők:	Ulas, Maciej Zygado, Jakub
Pályázati támogatás:	ANN-130909 OTKA K-115479 OTKA K-128088 OTKA
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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