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MIYAZAKI Takafumi
Department of Pure and Applied Science
Associate Professor
Last Updated :2024/05/13

Researcher Profile and Settings

Researcher

  • Name

    MIYAZAKI Takafumi

Profile and Settings

  • Name

    MIYAZAKI, Takafumi

Education

  • Apr. 2009, Mar. 2012, Tokyo Metropolitan University

Degree

  • Dr. Science

Association Memberships

  • THE MATHEMATICAL SOCIETY OF JAPAN

Research Experience

  • Oct. 2018, 9999, Gunma University, Graduate School of Science and Technology
  • Sep. 2015, Sep. 2018, Gunma University
  • Apr. 2013, Aug. 2015
  • Apr. 2012, Mar. 2013
  • Apr. 2012, Mar. 2016, Meiji Gakuin University, Faculty of Economics
  • Apr. 2011, Mar. 2012

Research Activities

Research Areas

  • Natural sciences, Algebra

Research Interests

  • exponential Diophantine equation
  • S-unit equation
  • system of Pellian equations

Published Papers

  • Number of solutions to a special type of unit equations in two unknowns, II, Takafumi Miyazaki , Istvan Pink, Apr. 2024, Research in Number Theory
  • Number of solutions to a special type of unit equations in two unknowns, Takafumi Miyazaki, Istvan Pink, Apr. 2024, American Journal of Mathematics, 146, 2, 295, 369
  • A purely exponential Diophantine equation in three unknowns, Takafumi Miyazaki, Masaki Sudo, Nobuhiro Terai, 10 Jul. 2021, Periodica Mathematica Hungarica, 84, 2, 287, 298
    DOI
  • Application of cubic residue theory to an exponential equation concerning Eisenstein triples, Takafumi Miyazaki, Oct. 2019, Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, 62, 110, 305, 312, Scientific journal
  • A study on the exponential Diophantine equation a^x+(a+b)^y=b^z, Takafumi Miyazaki,Nobuhiro Terai, Sep. 2019, Publicationes Mathematicae Debrecen, 95, 1-2, 19, 37, Scientific journal
    DOI
  • On Terai's exponential equation with two finite integer parameters, Takafumi Miyazaki, Mar. 2019, Notes on Number Theory and Discrete Mathematics, 25, 1, 84, 107, Scientific journal
    DOI
  • Coincidence between two binary recurrent sequences of polynomials arising from Diophantine triples, Takafumi Miyazaki, Dec. 2019, Tokyo Journal of Mathematics, 42, 2, 611, 619, Scientific journal
    DOI
  • ON JESMANOWICZ' CONJECTURE CONCERNING PRIMITIVE PYTHAGOREAN TRIPLES. II, T. Miyazaki,N. Terai, Dec. 2015, ACTA MATHEMATICA HUNGARICA, 147, 2, 286, 293, Scientific journal
    DOI
  • On the system of Diophantine equations (m^2-1)^r+b^2=c^2 and (m^2-1)^x+b^y=c^z, Takafumi Miyazaki,Florian Luca, Aug. 2015, JOURNAL OF NUMBER THEORY, 153, 321, 345, Scientific journal
    DOI
  • UPPER BOUNDS FOR SOLUTIONS OF AN EXPONENTIAL DIOPHANTINE EQUATION, Takafumi Miyazaki, 2015, ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 45, 1, 303, 344, Scientific journal
    DOI
  • A remark on Jesmanowicz' conjecture for the non-coprimality case, Takafumi Miyazaki, Aug. 2015, ACTA MATHEMATICA SINICA-ENGLISH SERIES, 31, 8, 1255, 1260, Scientific journal
    DOI
  • The regularity of Diophantine quadruples, Yasutsugu Fujita,Takafumi Miyazaki, Jun. 2018, Transactions of the American Mathematical Society, 370, 6, 3803, 3831, Scientific journal
    DOI
  • Contributions to some conjectures on a ternary exponential Diophantine equation, Takafumi Miyazaki, Oct. 2018, Acta Arithmetica, 186, 1, 1, 36, Scientific journal
    DOI
  • The shuffle variant of Terai's conjecture on exponential Diophantine equations, Takafumi Miyazaki, Sep. 2014, Publicationes Mathematicae Debrecen, 83, 1-2, 43, 62
    DOI
  • On the Diophantine equation ((c+1)m^2+1)^x+(cm^2-1)^y=(am)^z, Elif Kizildere,Takafumi Miyazaki,Gokhan Soydan, Sep. 2018, Turkish Journal of Mathematics, 42, 5, 2690, 2698, Scientific journal
    DOI
  • Jesmanowicz' conjecture on exponential Diophantine equations, Takafumi Miyazaki, Dec. 2011, Functiones et Approximatio Commentarii Mathematici, 45, 2, 207, 229
    DOI
  • Generalizations of classical results on Jesmanowicz' conjecture concerning Pythagorean triples, Takafumi Miyazaki, Feb. 2013, Journal of Number Theory, 133, 2, 583, 595
    DOI
  • On the equation 1^k+2^k+...+x^k=y^n for fixed x, Attila Berczes,Lajos Hajdu,Takafumi Miyazaki,Istvan Pink, Jun. 2016, Journal Number Theory, 163, 1, 43, 60
    DOI
  • On the Diophantine equation a^x+b^y=(a+2)^z, Takafumi Miyazaki,Alain Togbe,Pingzhi Yuan, Jun. 2016, Acta Mathematica Hungarica, 149, 1, 1, 9
    DOI
  • On the number of extensions of a Diophantine triple, Mihai Cipu,Yasutsugu Fujita,Takafumi Miyazaki, Apr. 2018, International Journal of Number Theory, 14, 3, 899, 917, Scientific journal
    DOI
  • A polynomial-exponential equation related to the Ramanujan-Nagell equation, Takafumi Miyazaki, Apr. 2018, The Ramanujan Journal, 45, 3, 601, 613, Scientific journal
    DOI
  • On the diophantine equation 1+x^a+z^b=y^n, Attila Berczes,Lajos Hajdu,Takafumi Miyazaki,Istvan Pink, 2016, Journal of Number Theory and Combinatorics, 8, 145, 154
  • On the exponential Diophantine equation (m^2+1)^x+(cm^2-1)^y=(am)^z, Miyazaki\, Takafumi,Terai\, Nobuhiro, Aug. 2014, Bulletin of the Australian Mathematical Society, 90, 1, 9-19.
    DOI
  • Jesmanowicz' Conjecture with Congruence Relations. II, Yasutsugu Fujita,Takafumi Miyazaki, Sep. 2014, Canadian Mathematical Bulletin, 57, 3, 495, 505
    DOI
  • Generalizations of classical results on Jesmanowicz' conjecture concerning Pythagorean triples II, Takafumi Miyazaki,Pingzhi Yuan,Danyao Wu, Aug. 2014, Journal of Number Theory, 141, 184, 201
    DOI
  • A note on the article by F. Luca "On the system of Diophantine equations a^2 + b^2 = (m^2+1)^r and a^x + b^y = (m^2+1)^z" (Acta Arith. 153 (2012), 373-392), Takafumi Miyazaki, Oct. 2014, Acta Arithmetica, 164, 1, 31, 42
    DOI
  • Jesmanowicz' conjecture with congruence relations, Yasutsugu Fujita,Takafumi Miyazaki, Nov. 2012, Colloquium Mathematicum, 128, 2, 211, 222
    DOI
  • The Diophantine equation (2am-1)^x+(2m)^y=(2am+1)^z, Takafumi Miyazaki,Alain Togbe, Dec. 2012, International Journal of Number Theory, 8, 8, 2035, 2044
    DOI
  • The shuffle variant of Jesmanowicz' conjecture concerning Pythagorean triples, Takafumi Miyazaki, Jun. 2011, Journal of the Australian Mathematical Society, 90, 3, 355, 370
    DOI
  • Terai's conjecture on exponential Diophantine equations, Takafumi Miyazaki, Jun. 2011, International Journal of Number Theory, 4, 4, 981, 999
    DOI
  • Exceptional cases of Terai's conjecture on Diophantine equations, Takafumi Miyazaki, Nov. 2010, Archiv der Mathematik, 95, 6, 519, 527
    DOI
  • On the conjecture of Jesmanowicz concerning Pythagorean triples, Takafumi Miyazaki, Dec. 2009, Bulletin of the Australian Mathematical Society, 80, 3, 413, 422
    DOI

MISC

  • Number of solutions to some purely exponential Diophantine equation in three unknowns, Takafumi Miyazaki, Jun. 2022, 2222, 212, 218
  • Number of solutions to a special type of unit equations in two variables II, Takafumi Miyazaki, Istvan Pink
  • Number of solutions to a special type of unit equations in two variables, Takafumi Miyazaki, Istvan Pink
  • On Terai's exponential equation with two finite integer parameters, 宮崎 隆史, Nov. 2018, 2092, 50, 59, Introduction scientific journal
  • Extendabilities of a Diophantine triple to quadruples, Yasutsugu Fujita,Takafumi Miyazaki, Jan. 2017, 2014, 111, 123, Introduction international proceedings
  • On the Nagell-Ljunggren equation, Noriko Hirata-Kohno,Tunde Kovacs,Takafumi Miyazaki, Dec. 2016, 2013, 60, 67, Introduction international proceedings
  • On an exponential equation concerning Pythagorean numbers with congruence relations, 宮崎 隆史, Dec. 2016, 2013, 50, 59, Introduction international proceedings
  • On an analogue of Jesmanowicz' conjecture on exponential Diophantine equations, 宮崎 隆史, Jan. 2014, 1874, 64, 70, Introduction international proceedings
  • Upper bounds for solutions of exponential Diophantine equations with applications to Fibonacci numbers, 宮崎 隆史, Jul. 2012, 1806, 134, 142, Introduction scientific journal
  • Exceptional cases of Terai's conjecture on Diophantine equations, Takafumi Miyazaki, 2011, DIOPHANTINE ANALYSIS AND RELATED FIELDS 2011 (DARF 2011), 1385, 87, 96, Introduction scientific journal
    DOI
  • On exponential Diophantine equations concerning Pythagorean triples, 宮崎 隆史, Aug. 2010, 1710, 113, 123, Introduction international proceedings
  • Generalizations of classical results on Jesmanowicz' conjecture concerning Pythagorean triples, 宮崎 隆史, 2010, 1264, 41, 51, Introduction scientific journal

Presentations

  • Number of solutions to a special type of unit equations in two unknowns III, Takafumi Miyazaki , Istvan Pink, Diophantine Analysis and Related Fields 2024, 05 Mar. 2024
  • Number of solutions to a special type of Pillai’s equation, Takafumi Miyazaki, Analytic number theory 2023, 13 Oct. 2023
  • Number of solutions to a special type of Pillai’s equation, Takafumi Miyazaki, 25th Central European Number Theory Conference, 31 Aug. 2023
  • Number of solutions to a special type of unit equations in two unknowns II, Takafumi Miyazaki, NUMBER THEORY SEMINAR, 25 Nov. 2022
  • Number of solutions to a special type of unit equations in two unknowns II, Takafumi Miyazaki, Darf seminar, 08 Oct. 2022
  • Number of solutions to a special type of unit equations in two unknowns II, 宮崎　隆史, Number Theory Conference 2022, 07 Jul. 2022, Hungary, International conference
  • 項数の少ない純指数型不定方程式について, 宮崎　隆史, 愛媛大学代数セミナー, 04 Feb. 2022
  • ある三変数の純指数型不定方程式の解の個数について, 宮崎　隆史, 解析的整数論とその周辺（2021年度RIMS共同研究（公開型））, 15 Oct. 2021, International conference
  • 三変数の純指数型不定方程式に関する Scott の定理について, 宮崎 隆史, 2021大分整数論研究集会, 03 Oct. 2021
  • 純指数型不定方程式 a^x+b^y=c^z の解の個数について, 宮崎　隆史, 日本数学会（2021年度秋季総合分科会）, 17 Sep. 2021
  • ベキ剰余理論の指数型不定方程式への応用, 宮崎 隆史, 大分数論セミナー, 10 Mar. 2019, Domestic conference
  • Application of cubic residue theory to a special type of unit equation concerning Eisenstein triples, Takafumi Miyazaki, Diophantine Analysis and Related Fields 2019, 09 Mar. 2019, 07 Mar. 2019, 09 Mar. 2019, Japan, International conference
  • 特別な単数方程式と立方剰余理論の応用, 宮崎 隆史, 九大代数学セミナー, 31 Jan. 2019, Domestic conference
  • 120 度三角形から生ずる三項指数型の不定方程式について その２, 宮崎 隆史, 群大桐生数論セミナー, 08 Dec. 2018, Domestic conference
  • Coincidence between two sequences of polynomials arising from Diophantine triples, Takafumi Miyazaki, Conference on Diophantine m-tuples and Related Problems II, 16 Oct. 2018, 15 Oct. 2018, 17 Oct. 2018, English, United States, International conference
  • 120 度三角形から生ずる三項指数型の不定方程式について, 宮崎 隆史, 群大桐生数論セミナー, 15 Dec. 2017
  • On Terai's exponential equation with two finite integer parameters, Takafumi Miyazaki, Analytic Number Theory and Related Areas, 01 Oct. 2017, English, International conference
  • Yuan による二次不定方程式に関する研究とその指数型不定方程式への応用, 宮崎 隆史, 松江セミナー, 27 Jan. 2017
  • Extension of Dem'janenko's classical work on a quadratic Diophantine equation and its applications, Takafumi Miyazaki, Diophantine Analysis and Related Fields 2017, 09 Jan. 2017, International conference
  • A polynomial-exponential equation related to the Ramanujan-Nagell equation, Takafumi Miyazaki, Computational Aspects of Diophantine Equations, 17 Feb. 2016, International conference
  • 原始ピタゴラス数から生ずる三項指数型不定方程式について, 宮崎 隆史, 代数学と計算, 14 Dec. 2015, Domestic conference
  • On a three-term exponential Diophantine equation, Takafumi Miyazaki, Journees Arithmetiques, 07 Jul. 2015, International conference
  • 連続するk乗数の和とSchafferの予想について, 宮崎 隆史, 日本数学会 春季総合分科会, 24 Mar. 2015, Domestic conference
  • A polynomial-exponential Diophantine equation related to the sum of consecutive k-th powers, Takafumi Miyazaki, Diophantine Analysis and Related Fields 2015, 05 Mar. 2015, International conference
  • On an exponential equation concerning Pythagorean numbers with congruence relations, Takafumi Miyazaki, Analytic Number Theory – Distribution and Approximation of Arithmetic Objects, 30 Oct. 2014, Domestic conference
  • 連続する k 乗数の和と Schaffer の予想, 宮崎 隆史, 明学セミナー, 18 Oct. 2014
  • On the exponential Diophantine equation a^x+b^y=c^z, 宮崎 隆史, Algebra and Number theory seminar (University of Debrecen), 11 Jun. 2014
  • 連立ディオファントス方程式 a^2+b^2=(m^2+1)^r と a^x+b^y=(m^2+1)^z について, 宮崎 隆史, 日本数学会 春季総合分科会, 18 Mar. 2014, Domestic conference
  • An explicit refinement of a theorem of F. Luca on Terai's conjecture, Takafumi Miyazaki, Diophantine Analysis and Related Fields 2014, 07 Mar. 2014, International conference
  • Jesmanowicz' conjecture concerning Pythagorean numbers, 宮崎 隆史, Number theory seminar （華南師範大学）, 31 Oct. 2013
  • ディオファントス方程式 (an-1)^x+n^y=(an+1)^z について, 宮崎 隆史, 第6 回若手ゼータ研究集会, 17 Feb. 2013
  • The Diophantine equation (an-1)^x+n^y=(an+1)^z, Takafumi Miyazaki, Diophantine Analysis and Related Fields 2013, 08 Jan. 2013, International conference
  • On an analogue of Jesmanowicz' conjecture on exponential Diophantine equations, Takafumi Miyazaki, Analytic Number Theory – Number Theory through Approximation and Asymptotics, 29 Oct. 2012, International conference
  • Upper bounds for solutions of exponential Diophantine equations with applications to Fibonacci numbers, Takafumi Miyazaki, Analytic Number Theory – related Multiple aspects of Arithmetic Functions, 01 Nov. 2011, International conference
  • 指数型不定方程式 a^x+b^y=c^z の解の大きさの評価について, 宮崎 隆史, 日本数学会 秋季総合分科会, 01 Oct. 2011, Domestic conference
  • Upper bounds for solutions of exponential Diophantine equations with applications to Fibonacci numbers, 宮崎 隆史, 鏡ヶ池の整数論セミナー, 16 Jul. 2011
  • 指数型不定方程式 a^x+b^y=c^z について, 宮崎 隆史, 整数論・力学系セミナー(弘前大学), 11 Jul. 2011
  • 指数型不定方程式 a^x+b^y=c^z の解の大きさの評価について, 宮崎 隆史, 首都大整数論セミナー, 28 Jun. 2011
  • 指数型不定方程式a^x+b^y=c^z の解の大きさの評価について, 宮崎 隆史, 明学セミナー, 18 Jun. 2011
  • Exceptional cases of Terai's conjecture on Diophantine equations, Takafumi Miyazaki, Diophantine Analysis and Related Fields 2011, 04 Mar. 2011, International conference
  • 不定方程式における寺井予想の例外ケースについて, 宮崎 隆史, 第4 回若手ゼータ研究集会, 23 Feb. 2011
  • Terai's conjecture on exponential Diophantine equations, Takafumi Miyazaki, Analytic Number Theory — through Value Distribution and other Properties of Analytic Functions, 07 Oct. 2010, International conference
  • Generalizations of classical results on Jesmanowicz' conjecture concerning Pythagorean triples, 宮崎 隆史, 鏡ヶ池の整数論セミナー, 19 Jun. 2010
  • ピタゴラス数に関する Jesmanowicz 予想の古典的な結果の一般化, 宮崎 隆史, 学習院土曜セミナー, 05 Mar. 2010
  • Generalizations of classical results on Jesmanowicz' conjecture concerning Pythagorean triples, Takafumi Miyazaki, Diophantine Analysis and Related Fields 2010, 04 Mar. 2010, International conference
  • On exponential Diophantine equations concerning Pythagorean triples, Takafumi Miyazaki, Analytic number theory and related topics, 15 Oct. 2009, International conference
  • 指数型不定方程式における Jesmanowicz の予想について, 宮崎 隆史, 鏡ヶ池の整数論セミナー, 27 Jun. 2009
  • 指数型不定方程式における Jesmanowicz の予想について, 宮崎 隆史, 早稲田大学整数論セミナー, 19 Jun. 2009
  • ピタゴラス数に関するJesmanowicz 予想について, 宮崎 隆史, 首都大整数論セミナー, 08 Jul. 2008

Research Projects

  • Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Gunma University, Apr. 2020, Mar. 2024, 20K03553
  • Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B), Grant-in-Aid for Young Scientists (B), Gunma University, Apr. 2016, Mar. 2020, 16K17557
  • Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows, Grant-in-Aid for JSPS Fellows, Apr. 2013, Mar. 2016, 13J00484
  • Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows, Grant-in-Aid for JSPS Fellows, Tokyo Metropolitan University, Apr. 2011, Mar. 2012, 11J05674

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