ON A FAMILY OF TWO-PARAMETRIC D(4)-TRIPLES

被引：0

作者：

Filipin, Alan ^{[1
]}

He, Bo ^{[2
]}

Togbe, Alain ^{[3
]}

机构：

[1] Univ Zagreb, Fac Civil Engn, Zagreb 10000, Croatia

[2] ABa Teachers Coll, Dept Math, Wenchuan 623000, Sichuan, Peoples R China

[3] Purdue Univ N Cent, Dept Math, Westville, IN 46391 USA

来源：

GLASNIK MATEMATICKI | 2012年 / 47卷 / 01期

关键词：

Diophantine m-tuples; Pell equations; Baker's method; DIOPHANTINE; THEOREM; NUMBER; SETS; K-1;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let k be a positive integer. In this paper, we study a parametric family of the sets of integers {k,A(2)k + 4A, (A + 1)(2)k + 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 = (A(4) broken vertical bar 2A(3) broken vertical bar A(2))k(3) broken vertical bar (8A(3) broken vertical bar 12A(2) broken vertical bar 4A)k(2) broken vertical bar (20A(2) broken vertical bar 20A broken vertical bar 4)k broken vertical bar (16A broken vertical bar 8) for 1 <= A <= 22 and A >= 51767.

引用

页码：31 / 51

页数：21

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