ON MONOCHROMATIC LINEAR RECURRENCE SEQUENCES

被引：0
|
作者：
Bertok, Csanad [1 ]
Nyul, Gabor [1 ]
机构：
[1] Univ Debrecen, Inst Math, POB 12, H-4010 Debrecen, Hungary
来源：
CONTRIBUTIONS TO DISCRETE MATHEMATICS | 2017年 / 11卷 / 02期
基金：
匈牙利科学研究基金会;
关键词：
linear recurrence sequences; van der Waerden type theorems;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we prove some van der Waerden type theorems for linear recurrence sequences. Under the assumption a(i-1) <= a(i)a(s-1) (i = 2, . . . , s), we extend results of G. Nyul and B. Rauf for sequences satisfying x(i) = a(1)x(i-s) + . . . + a(s)x(i-1) (i >= s + 1), where a(1), . . . , a(s) are positive integers. Moreover, we solve completely the same problem for sequences satisfying the binary recurrence relation x(i) = ax(i-1) - bx(i-2) (i >= 3) and x(1) < x(2), where a, b are positive integers with a >= b vertical bar 1.
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页码：58 / 62
页数：5
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