A note on balancing binomial coefficients

被引：0
|
作者：
Chern, Shane [1 ]
机构：
[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China
来源：
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2015年 / 91卷 / 08期
关键词：
Balancing problem; binomial coefficient; linear form in elliptic logarithms; ELLIPTIC DIOPHANTINE EQUATIONS;
D O I：
10.3792/pjaa.91.110
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In 2014, T. Komatsu and L. Szalay studied the balancing binomial coefficients. In this paper, we focus on the following Diophantine equation (GRAPHICS) where y > x> 5 are integer unknowns. We prove that the only integral solution is (x, y) = (14,15). Our method is mainly based on the linear form in elliptic logarithms.
引用
收藏
页码：110 / 111
页数：2
相关论文
共 50 条
  • [31] ON CONGRUENCES FOR BINOMIAL COEFFICIENTS
    YEUNG, KM
    JOURNAL OF NUMBER THEORY, 1989, 33 (01) : 1 - 17
  • [32] GEOMETRY OF BINOMIAL COEFFICIENTS
    WOLFRAM, S
    AMERICAN MATHEMATICAL MONTHLY, 1984, 91 (09): : 566 - 571
  • [33] On the divisibility of binomial coefficients
    Casacuberta, Silvia
    ARS MATHEMATICA CONTEMPORANEA, 2020, 19 (02) : 297 - 309
  • [34] A GENERALIZATION OF THE BINOMIAL COEFFICIENTS
    LOEB, DE
    DISCRETE MATHEMATICS, 1992, 105 (1-3) : 143 - 156
  • [35] On a generalization of binomial coefficients
    Jouhet, F
    Lass, B
    Zeng, J
    ELECTRONIC JOURNAL OF COMBINATORICS, 2004, 11 (01):
  • [36] More binomial coefficients
    Santmyer, JM
    AMERICAN MATHEMATICAL MONTHLY, 1997, 104 (02): : 179 - 179
  • [37] SUMMATIONS OF BINOMIAL COEFFICIENTS
    CARLITZ, L
    AMERICAN MATHEMATICAL MONTHLY, 1967, 74 (05): : 595 - &
  • [38] On an Identity with Binomial Coefficients
    E. A. Karatsuba
    Mathematical Notes, 2019, 105 : 145 - 147
  • [39] Bisecting binomial coefficients
    Ionascu, Eugen J.
    Martinsen, Thor
    Stanica, Pantelimon
    DISCRETE APPLIED MATHEMATICS, 2017, 227 : 70 - 83
  • [40] LCM OF BINOMIAL COEFFICIENTS
    BREUSCH, R
    AMERICAN MATHEMATICAL MONTHLY, 1979, 86 (02): : 131 - 131
12345