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

Abstract

Abstract. Let k be a positive integer. In this paper, we study a parametric family of the sets of integersWe 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, thenfor 1 ≤ A ≤ 22 and A ≥ 51767.

Two-parameter families of uniquely extendable Diophantine triples

“…The result published in [22] for the ε = 1 case says that the conclusion of our Theorem 1 holds for either A ≤ 10 or A ≥ 52330. Similar results have been published in [17] for ε = 2. More precisely, the statement has been proved for A ≤ 22 as well as for A ≥ 51767.…”

“…Proof. Follow the proof of Lemma 6 from [17] with a twist on the final stepuse A + 1 + 2 · K −1 instead of A + 3 as an upper bound for c/a.…”

Explication of Dio 3 -Tuples from Truncated Octahedral Number-I

“…[1][2][3] has been referred for multitudinal ideas on number theory. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] has been studied for numerous ideas on diophantine triples. In this paper we attempt to explicate dio 3-tuples from truncated octahedral number of different ranks.…”

On the torsion group of elliptic curves induced by D(4)-triples

“…Dujella and Ramasamy [9] generalized this result to the parametric family of D(4)-quadruples {F 2k , 5F 2k , 4F 2k+2 , 4L 2k F 4k+2 } involving Fibonacci and Lucas numbers. Other generalization to a two-parametric family of D(4)-triples can be found in [13]. Dujella [6] proved that there does not exist a D(1)-sextuple and that there are only finitely many D(1)-quintuples.…”