MIYAZAKI Takafumi
| Department of Pure and Applied Science | Associate Professor |
Last Updated :2026/07/04
■Researcher basic information
Researcher
Name
MIYAZAKI Takafumi
Profile and Settings
Name
MIYAZAKI, Takafumi
Affiliation
所属情報
Graduate School of Science and TechnologyJob title
Associate Professor
Research History
■Research activity information
Papers
- General sharp bounds for the number of solutions to purely exponential equations with three terms, Maohua Le, Takafumi Miyazaki, Yes, Yes, 27 Jan. 2026, The Quarterly Journal of Mathematics, 77, 1, 129, 149
- Number of solutions to a special type of unit equations in two unknowns, III, Takafumi Miyazaki, Istvan Pink, Yes, Yes, 07 Aug. 2025, Mathematical Proceedings of the Cambridge Philosophical Society, 179, 3, 737, 784
- Number of solutions to a special type of unit equations in two unknowns, II, Takafumi Miyazaki , Istvan Pink, Yes, Yes, Apr. 2024, Research in Number Theory
- Number of solutions to a special type of unit equations in two unknowns, Takafumi Miyazaki, Istvan Pink, Yes, Yes, Apr. 2024, American Journal of Mathematics, 146, 2, 295, 369
- A purely exponential Diophantine equation in three unknowns, Takafumi Miyazaki, Masaki Sudo, Nobuhiro Terai, Yes, 10 Jul. 2021, Periodica Mathematica Hungarica, 84, 2, 287, 298
- Application of cubic residue theory to an exponential equation concerning Eisenstein triples, Takafumi Miyazaki, Yes, Yes, Yes, 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, No, Sep. 2019, Publicationes Mathematicae Debrecen, 95, 1-2, 19, 37, Scientific journal
- On Terai's exponential equation with two finite integer parameters, Takafumi Miyazaki, Yes, Yes, Yes, Mar. 2019, Notes on Number Theory and Discrete Mathematics, 25, 1, 84, 107, Scientific journal
- Coincidence between two binary recurrent sequences of polynomials arising from Diophantine triples, Takafumi Miyazaki, Yes, Yes, Yes, Dec. 2019, Tokyo Journal of Mathematics, 42, 2, 611, 619, Scientific journal
- ON JESMANOWICZ' CONJECTURE CONCERNING PRIMITIVE PYTHAGOREAN TRIPLES. II, T. Miyazaki,N. Terai, Dec. 2015, ACTA MATHEMATICA HUNGARICA, 147, 2, 286, 293, Scientific journal
- 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
- UPPER BOUNDS FOR SOLUTIONS OF AN EXPONENTIAL DIOPHANTINE EQUATION, Takafumi Miyazaki, 2015, ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 45, 1, 303, 344, Scientific journal
- 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
- The regularity of Diophantine quadruples, Yasutsugu Fujita,Takafumi Miyazaki, No, Jun. 2018, Transactions of the American Mathematical Society, 370, 6, 3803, 3831, Scientific journal
- Contributions to some conjectures on a ternary exponential Diophantine equation, Takafumi Miyazaki, Yes, Yes, Yes, Oct. 2018, Acta Arithmetica, 186, 1, 1, 36, Scientific journal
- The shuffle variant of Terai's conjecture on exponential Diophantine equations, Takafumi Miyazaki, Sep. 2014, Publicationes Mathematicae Debrecen, 83, 1-2, 43, 62
- On the Diophantine equation ((c+1)m^2+1)^x+(cm^2-1)^y=(am)^z, Elif Kizildere,Takafumi Miyazaki,Gokhan Soydan, No, Sep. 2018, Turkish Journal of Mathematics, 42, 5, 2690, 2698, Scientific journal
- Jesmanowicz' conjecture on exponential Diophantine equations, Takafumi Miyazaki, Dec. 2011, Functiones et Approximatio Commentarii Mathematici, 45, 2, 207, 229
- Generalizations of classical results on Jesmanowicz' conjecture concerning Pythagorean triples, Takafumi Miyazaki, Feb. 2013, Journal of Number Theory, 133, 2, 583, 595
- 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
- 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
- On the number of extensions of a Diophantine triple, Mihai Cipu,Yasutsugu Fujita,Takafumi Miyazaki, No, Apr. 2018, International Journal of Number Theory, 14, 3, 899, 917, Scientific journal
- A polynomial-exponential equation related to the Ramanujan-Nagell equation, Takafumi Miyazaki, Yes, Yes, Yes, Apr. 2018, The Ramanujan Journal, 45, 3, 601, 613, Scientific journal
- 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.
- Jesmanowicz' Conjecture with Congruence Relations. II, Yasutsugu Fujita,Takafumi Miyazaki, Sep. 2014, Canadian Mathematical Bulletin, 57, 3, 495, 505
- 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
- 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
- Jesmanowicz' conjecture with congruence relations, Yasutsugu Fujita,Takafumi Miyazaki, Nov. 2012, Colloquium Mathematicum, 128, 2, 211, 222
- 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
- The shuffle variant of Jesmanowicz' conjecture concerning Pythagorean triples, Takafumi Miyazaki, Jun. 2011, Journal of the Australian Mathematical Society, 90, 3, 355, 370
- Terai's conjecture on exponential Diophantine equations, Takafumi Miyazaki, Jun. 2011, International Journal of Number Theory, 4, 4, 981, 999
- Exceptional cases of Terai's conjecture on Diophantine equations, Takafumi Miyazaki, Nov. 2010, Archiv der Mathematik, 95, 6, 519, 527
- On the conjecture of Jesmanowicz concerning Pythagorean triples, Takafumi Miyazaki, Dec. 2009, Bulletin of the Australian Mathematical Society, 80, 3, 413, 422
Misc.
- Number of solutions to a special type of Pillai's equation, Takafumi Miyazaki, Jun. 2024, 2285, 200, 208
- Number of solutions to some purely exponential Diophantine equation in three unknowns, Takafumi Miyazaki, Jun. 2022, 2222, 212, 218
- Nov. 2018, 2092, 50, 59, Introduction scientific journal
- Jan. 2017, 2014, 111, 123, Introduction international proceedings
- Dec. 2016, 2013, 60, 67, Introduction international proceedings
- Dec. 2016, 2013, 50, 59, Introduction international proceedings
- Jan. 2014, 1874, 64, 70, Introduction international proceedings
- 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
- Aug. 2010, 1710, 113, 123, Introduction international proceedings
- 2010, 1264, 41, 51, Introduction scientific journal
Presentations
- Purely exponential Diophantine equation a^x+b^y=c^z has at most 1 positive solution in most cases, Takafumi Miyazaki, Diophantine Analysis and Related Fields 2026, 10 Mar. 2026
- Applications of Baker’s method to purely exponential Diophantine equations beyond three terms, Takafumi Miyazaki, Analytic Number Theory and Special Functions, 10 Dec. 2025
- 06 Dec. 2025
- 19 Oct. 2024
- Number of solutions to a special type of unit equations in two unknowns III, Takafumi Miyazaki, NUMBER THEORY SEMINAR, 15 Jun. 2024
- 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, Number Theory Conference 2022, 07 Jul. 2022, Hungary, International conference
- 04 Feb. 2022
- 15 Oct. 2021, International conference
- 03 Oct. 2021
- 17 Sep. 2021
- 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
- 31 Jan. 2019, Domestic conference
- 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
- 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
- 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
- 14 Dec. 2015, Domestic conference
- On a three-term exponential Diophantine equation, Takafumi Miyazaki, Journees Arithmetiques, 07 Jul. 2015, International conference
- 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
- 18 Oct. 2014
- 11 Jun. 2014
- 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
- 31 Oct. 2013
- 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
- 01 Oct. 2011, Domestic conference
- 16 Jul. 2011
- 11 Jul. 2011
- 28 Jun. 2011
- 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
- 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
- 19 Jun. 2010
- 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
- 27 Jun. 2009
- 19 Jun. 2009
- 08 Jul. 2008
Research Projects
- Takafumi Miyazaki, Japan Society for the Promotion of Science, Apr. 2024, Mar. 2029, Principal investigator, 24K06642
- 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, url
- 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, url
- 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, url
- 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. 2013, 11J05674, url
