Arithmetic Progressions in the Values of a Quadratic Polynomial

被引：0

作者：

Pongsriiam, Prapanpong ^{[1
]}

Subwattanachai, Kittipong ^{[2
]}

机构：

[1] Silpakorn Univ, Dept Math, Fac Sci, Nakhon Pathom 73000, Thailand

[2] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furo Cho, Nagoya, Aichi 4648602, Japan

来源：

AMERICAN MATHEMATICAL MONTHLY | 2021年

关键词：

Primary; 11B25; Secondary; 11C08; 11D09; FIBONACCI; NUMBERS;

D O I：

10.1080/00029890.2021.1977884

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well known that arithmetic progressions of squares have length at most 3. In this note, we extend the result to the case of quadratic polynomials.

引用

页数：5

共 50 条

[1] ON VALUES OF A POLYNOMIAL AT ARITHMETIC PROGRESSIONS WITH EQUAL PRODUCTS
SARADHA, N
SHOREY, TN
TIJDEMAN, R
[J]. ACTA ARITHMETICA, 1995, 72 (01) : 67 - 76
[2] THE SUM OF DIGITS OF POLYNOMIAL VALUES IN ARITHMETIC PROGRESSIONS
Stoll, Thomas
[J]. FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2012, 47 (02) : 233 - 239
[3] Arithmetic progressions in polynomial orbits
Sadek, Mohammad
Wafik, Mohamed
Yesin, Tugba
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2024, 20 (08) : 2009 - 2025
[4] MEAN QUADRATIC VALUES OF ARITHMETIC PROGRESSIONS OF THE FOURIER COEFFICIENTS OF PARABOLIC FORMS
AKBAROV, MK
[J]. DOKLADY AKADEMII NAUK SSSR, 1981, 261 (03): : 521 - 523
[5] ARITHMETIC PROGRESSIONS IN CYCLES OF QUADRATIC POLYNOMIALS
Erkama, Timo
[J]. REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 2009, 54 (5-6): : 441 - 450
[6] Arithmetic Progressions and binary quadratic forms
Alaca, Ayse
Alaca, Saban
Williams, Kenneth S.
[J]. AMERICAN MATHEMATICAL MONTHLY, 2008, 115 (03): : 252 - 254
[7] On values of a polynomial at arithmetic progressions with equal products (vol 72, pg 67, 1995)
Saradha, N
Shorey, TN
Tijdeman, R
[J]. ACTA ARITHMETICA, 1998, 84 (04) : 385 - 386
[8] The distribution of quadratic residues and nonresidues in arithmetic progressions
Justus, Benjamin
[J]. LITHUANIAN MATHEMATICAL JOURNAL, 2014, 54 (02) : 142 - 149
[9] The distribution of quadratic residues and nonresidues in arithmetic progressions
Benjamin Justus
[J]. Lithuanian Mathematical Journal, 2014, 54 : 142 - 149
[10] Integral quadratic forms avoiding arithmetic progressions
Earnest, A. G.
Kim, Ji Young
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2020, 16 (10) : 2141 - 2148

← 1 2 3 4 5 →