A NOTE ON SIERPINSKI'S PROBLEM RELATED TO TRIANGULAR NUMBERS

被引：2
|
作者：
Ulas, Maciej [1 ]
机构：
[1] Jagiellonian Univ, Inst Math, PL-30348 Krakow, Poland
来源：
COLLOQUIUM MATHEMATICUM | 2009年 / 117卷 / 02期
关键词：
triangular numbers; Sierpinski's problem; rational points; diophantine equations;
D O I：
10.4064/cm117-2-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the system of equations t(x) +t(y) = t(p), t(y) +t(z) = t(q), t(x) + t(z) = t(r), where t(x) = x(x + 1)/2 is a triangular number, has infinitely many solutions in integers. Moreover, we show that this system has a rational three-parameter solution. Using this result we show that the system t(x) + t(y) = t(p), t(y) + t(z) = t(q), t(x) + t(z) = t(r), t(x) + t(y) +t(z) = t(s) has infinitely many rational two-parameter solutions.
引用
收藏
页码：165 / 173
页数：9
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