Terai Nobuhiro 寺井伸浩

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TERAI Nobuhiro 寺井伸浩

寺井伸浩テライノブヒロ

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Researcher Number	00236978
Other IDs
Affiliation (Current)	2025: 大分大学, 理工学部, 教授
Affiliation (based on the past Project Information) *help	2017 – 2023: 大分大学, 理工学部, 教授 2014 – 2016: 大分大学, 工学部, 教授 2013: 足利工業大学, 工学部, 准教授 2010: 足利工業大学, 準教授 1994: 足利工業大学, 工学部, 講師
Review Section/Research Field	Principal Investigator Basic Section 11010:Algebra-related / Algebra Except Principal Investigator Algebra / Algebra
Keywords	Principal Investigator 一般化されたFermat方程式 / Baker理論 / Jesmanowicz予想 / 指数型不定方程式 / Ramanujan-Nagell方程式 / 楕円曲線 / 整数解 / 一般化された Fermat 方程式 / Ｂaker理論 / 不定方程式 / 数論 / Terai予想 … More Except Principal Investigator … More 整数点 / 楕円曲線 / クロアチア：アメリカ：ルーマニア / ルーマニア・クロアチア・アメリカ / 国際情報交換 / ディオファンタスの m 組 / 楕円曲線の整数点 / 楕円曲線の Mordell-Weil 群 / 連立ペル方程式 / 生成元 / モーデルヴェイユ群 / 不定方程式 / 有理点 / Mordell-weil群 / アーベル曲面 / 代数体 / モルデル・ヴェイユ群 / 類数 / トーション / アーベル多様体 / 虚数乗法 / 中山の予想 / 表現論 / 局所環 / コホモロジー / 多元環 Less

Study on the generalized Ramanujan-Nagell equationsPrincipal Investigator
- Principal Investigator
  
  寺井伸浩
- Project Period (FY)
  2022 – 2024
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Oita University
Study on exponential Diophantine equations related to Jesmanowicz' conjecturePrincipal Investigator
- Principal Investigator
  
  Terai Nobuhiro
- Project Period (FY)
  2018 – 2022
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Oita University
Study on integer solutions of exponential Diophantine equationsPrincipal Investigator
- Principal Investigator
  
  Terai Nobuhiro
- Project Period (FY)
  2015 – 2017
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Oita University
Rational points and integer points on elliptic curves and the related Diophantine equations
- Principal Investigator
  
  FUJITA Yasutsugu
- Project Period (FY)
  2013 – 2015
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nihon University
Complex multiplication of elliptic curves and abelian varieties
- Principal Investigator
  
  NAKAMURA Tetsuo
- Project Period (FY)
  2008 – 2010
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Tohoku University
多元環の表現論および関連する分野の研究
- Principal Investigator
  
  太刀川弘幸
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Ashikaga Institute of Technology

All 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2013 2011 2009 Other

All Journal Article Presentation

[Journal Article] A note on the ternary purely exponential Diophantine equation f^x+(f+g)^y=g^z2023
- Author(s)
  Yasutsugu Fujita, Maohua Le, Nobuhiro Terai
- Journal Title
  
  Tsukuba J. Math.
  
  Volume: 47 Issue: 1 Pages: 113-123
- DOI
  10.21099/tkbjm/20234701113
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-22K03271
[Journal Article] A note on the solution to the generalized Ramanujan-Nagell equation x^2 + (4c)^y = (c + 1)^z2023
- Author(s)
  Yasutsugu Fujita, Maohua Le, Nobuhiro Terai
- Journal Title
  
  Indian Journal of Pure and Applied Math.
  
  Volume: 54 Issue: 4 Pages: 1145-1157
- DOI
  10.1007/s13226-022-00328-4
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-22K03271
[Journal Article] A note on the number of solutions of ternary purely exponential Diophantine equations2023
- Author(s)
  Yasutsugu Fujita, Maohua Le, Nobuhiro Terai
- Journal Title
  
  Bull. Australian Math. Soc.
  
  Volume: 107 Issue: 1 Pages: 53-65
- DOI
  10.1017/s0004972722000508
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-22K03271
[Journal Article] On the generalized Ramanujan-Nagell equation x^2+b^m=c^n with a^2+b^r=c^22022
- Author(s)
  Nobuhiro Terai, Saya Nakashiki and Yudai Suenaga
- Journal Title
  
  SUT Journal of Mathematics
  
  Volume: 58 Issue: 1 Pages: 77-89
- DOI
  10.55937/sut/1654320039
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-18K03247
[Journal Article] On the generalized Ramanujan-Nagell equation x^2 + (4c)^m = (c + 1)^n2022
- Author(s)
  Nobuhiro Terai, Saya Nakashiki and Yudai Suenaga
- Journal Title
  
  International Mathematical Forum
  
  Volume: 17 Issue: 1 Pages: 1-10
- DOI
  10.12988/imf.2022.912300
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-18K03247
[Journal Article] Some exponential Diophantine equations attached to Pythagorean triples2022
- Author(s)
  Yasutsugu Fujita, Maohua Le and Nobuhiro Terai
- Journal Title
  
  Bull. Math. Soc. Sci. Math. Roumanie
  
  Volume: 65 Pages: 359-365
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-22K03271
[Journal Article] On exponential Diophantine equations concerning Pythagorean triples2022
- Author(s)
  Nobuhiro Terai and Yasutsugu Fujita
- Journal Title
  
  Publicationes Mathematicae Debrecen
  
  Volume: 101 Issue: 1-2 Pages: 147-168
- DOI
  10.5486/pmd.2022.9213
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22K03271
[Journal Article] On the Diophantine equation x^2 + b^m = c^n with a^2 + b^4 = c^22022
- Author(s)
  Nobuhiro Terai
- Journal Title
  
  Indian Journal of Pure and Applied Mathematics
  
  Volume: 53 Issue: 1 Pages: 162-169
- DOI
  10.1007/s13226-021-00162-0
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03247
[Journal Article] On the exponential Diophantine equation (4m^2 + 1)^x + (45m^2 － 1)^y = (7m)^z,2021
- Author(s)
  Nobuhiro Terai and Yoshiki Shinsho
- Journal Title
  
  Int. J. Algebra
  
  Volume: 15 Issue: 4 Pages: 233-241
- DOI
  10.12988/ija.2021.91567
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-18K03247
[Journal Article] A purely exponential Diophantine equation in three unknowns2021
- Author(s)
  Miyazaki Takafumi、Sudo Masaki、Terai Nobuhiro
- Journal Title
  
  Periodica Mathematica Hungarica
  
  Volume: 84 Issue: 2 Pages: 287-298
- DOI
  10.1007/s10998-021-00405-x
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20K03553, KAKENHI-PROJECT-18K03247
[Journal Article] On the generalized Ramanujan-Nagell equation x^2 + (2c － 1)^m = c^n2020
- Author(s)
  Yasutsugu Fujita, Nobuhiro Terai
- Journal Title
  
  Acta Math. Hungar.
  
  Volume: 162 Issue: 2 Pages: 518-526
- DOI
  10.1007/s10474-020-01085-8
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03247
[Journal Article] On the exponential Diophantine equation (4m^2 + 1)^x + (21m^2 － 1)^y = (5m)^z2020
- Author(s)
  Nobuhiro Terai
- Journal Title
  
  Annales Mathematicae et Informaticae
  
  Volume: 52 Pages: 243-253
- DOI
  10.33039/ami.2020.01.003
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03247
[Journal Article] On the exponential Diophantine equation (3m^2 + 1)^x + (qm^2 － 1)^y = (rm)^z2020
- Author(s)
  Nobuhiro Terai, Yoshiki Shinsho
- Journal Title
  
  SUT J. Math.
  
  Volume: 56 Pages: 147-158
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03247
[Journal Article] A study on the exponential Diophantine equation a^x + (a + b)^y = b^z2019
- Author(s)
  Takafumi Miyazaki, Nobuhiro Terai
- Journal Title
  
  Publ. Math. Debrecen
  
  Volume: 95 Issue: 1-2 Pages: 19-37
- DOI
  10.5486/pmd.2019.8283
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03247
[Journal Article] On the exponential Diophantine equation (3pm^2-1)^x+(p(p-3)m^2+1)^y=(pm)^z2017
- Author(s)
  Nobuhiro Terai, Takeshi Hibino
- Journal Title
  
  Period. Math. Hungar.
  
  Volume: 74 Issue: 2 Pages: 227-234
- DOI
  10.1007/s10998-016-0162-z
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K04786
[Journal Article] On the exponential Diophantine equation a^x+lb^y=c^z2016
- Author(s)
  Nobuhiro Terai, Takeshi Hibino
- Journal Title
  
  Int. J. Algebra
  
  Volume: 10 Pages: 393-403
- DOI
  10.12988/ija.2016.6747
- Peer Reviewed / Acknowledgement Compliant / Open Access
- Data Source
  KAKENHI-PROJECT-15K04786
[Journal Article] On Jesmanowicz' conjecture concerning primitive Pythagorean triples II2015
- Author(s)
  Nobuhiro Terai, Takafumi Miyazaki
- Journal Title
  
  Acta Math. Hungarica
  
  Volume: 147 Issue: 2 Pages: 286-293
- DOI
  10.1007/s10474-015-0552-3
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-15K04786, KAKENHI-PROJECT-13J00484
[Journal Article] On the exponential Diophantine equation (12m^2 + 1)^x + (13m^2-1)^y = (5m)^z2015
- Author(s)
  Nohuhiro Terai, Takeshi Hibino
- Journal Title
  
  International Journal of Algebra
  
  Volume: 9 Pages: 261-272
- DOI
  10.12988/ija.2015.5529
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-15K04786
[Journal Article] On exponential Diophantine equations containing the Euler quotient2015
- Author(s)
  Nobuhiro Terai
- Journal Title
  
  Bull. Australian Math. Soc.
  
  Volume: 91 Issue: 1 Pages: 11-18
- DOI
  10.1017/s0004972714000719
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K04786
[Journal Article] Generators and integer points on the elliptic curve y^2=x^3-nx2013
- Author(s)
  Yasutsugu Fujita and Nobuhiro Terai
- Journal Title
  
  Acta Arithmetica
  
  Volume: 160 Issue: 4 Pages: 333-348
- DOI
  10.4064/aa160-4-3
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-25400025
[Journal Article] Integer points and independent points on ellpitic curve y^2=x^3-p^k x2011
- Author(s)
  Y.Fujita, N.Terai
- Journal Title
  
  Tokyo J.Math
  
  Volume: (受理済)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540004
[Journal Article] Integer points and independent points on the elliptic curve y^2=x^3-p^kx
- Author(s)
  Y.Fujita, N.Terai
- Journal Title
  
  J.Math. (accepted)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540004
[Presentation] いろいろな指数型不定方程式の解の個数2024
- Author(s)
  寺井伸浩
- Organizer
  数理情報科学さくらセミナー2024 (於鹿児島大学理学部）
- Invited
- Data Source
  KAKENHI-PROJECT-22K03271
[Presentation] Ramanujanと関係する指数型不定方程式2023
- Author(s)
  寺井伸浩
- Organizer
  第15回福岡数論研究集会 (於立命館アジア太平洋大学)
- Invited
- Data Source
  KAKENHI-PROJECT-22K03271
[Presentation] ラマヌジャンのタクシー数 1729 に関する不定方程式2023
- Author(s)
  寺井伸浩
- Organizer
  数理情報科学さくらセミナー2023（於鹿児島大学理学部）
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] 一般化されたRamanujan-Nagell方程式 x^2 + b^m=c^n について2022
- Author(s)
  寺井伸浩
- Organizer
  第14回福岡数論研究集会 (於九州大学伊都キャンパス)
- Invited
- Data Source
  KAKENHI-PROJECT-22K03271
[Presentation] On the generalized Ramanujan-Nagell equation x^2 + (c^2 － 1)^m = c^n2021
- Author(s)
  寺井伸浩
- Organizer
  第144 回日本数学会九州支部例会
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] ラマヌジャンを楽しむ - 指数型不定方程式の不思議な世界2021
- Author(s)
  寺井伸浩
- Organizer
  数理情報科学さくらセミナー2021 (於鹿児島大学理学部+Zoomによるオンライン開催)
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] ラマヌジャンのタクシー数1729 の不思議.2021
- Author(s)
  寺井伸浩
- Organizer
  数理情報科学さくらセミナー2021 (於鹿児島大学理学部+Zoomによるオンライン開催)
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] 約数関数σ(n) とオイラー関数φ(n) を含む不定方程式の整数解について2020
- Author(s)
  寺井伸浩
- Organizer
  日本応用数理学会第16 回研究部会連合発表会(於中央大後楽園キャンパス)
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] On the Diophantine equation x^2+b^m=c^n with a^2+b^4=c^22019
- Author(s)
  寺井伸浩
- Organizer
  大分数論セミナー
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] 指数型不定方程式 a^x + b^y = c^z について2019
- Author(s)
  寺井伸浩
- Organizer
  松江数論セミナー
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] 指数型不定方程式 a^x + b^y = c^z と x^2 + b^m = c^n の最近の進展について2019
- Author(s)
  寺井伸浩
- Organizer
  第64 回代数学シンポジウム (於東北大学大学院情報科学研究科棟)
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] ピタゴラスから拡がる指数型不定方程式の世界2019
- Author(s)
  寺井伸浩
- Organizer
  数理情報科学さくらセミナー2019
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] 階乗と冪を含む不定方程式について2018
- Author(s)
  寺井伸浩
- Organizer
  北陸数論セミナー
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] 指数型不定方程式 (3pm^2-1)^x+(p(p-3)m^2+1)^y=(pm)^z について2018
- Author(s)
  寺井伸浩
- Organizer
  第139回日本数学会九州支部例会
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] On the generalized Ramanujan-Nagell equation x^2 + (2c-1)^m = c^n2018
- Author(s)
  寺井伸浩
- Organizer
  群大桐生数論セミナー
- Invited
- Data Source
  KAKENHI-PROJECT-18K03247
[Presentation] 一般化されたRamanujan-Nagell方程式 x^2+(2c-1)^m=c^n について2018
- Author(s)
  寺井伸浩
- Organizer
  第138回日本数学会九州支部例会
- Data Source
  KAKENHI-PROJECT-15K04786
[Presentation] 指数型不定方程式 a^x+lb^y=c^z について2017
- Author(s)
  寺井伸浩
- Organizer
  第136回日本数学会九州支部例会
- Place of Presentation
  福岡教育大学(福岡県福岡市）
- Year and Date
  2017-02-18
- Data Source
  KAKENHI-PROJECT-15K04786
[Presentation] On the exponential Diophantine equation a^x + b^y = c^z2017
- Author(s)
  寺井伸浩
- Organizer
  第11回福岡数論研究集会
- Data Source
  KAKENHI-PROJECT-15K04786
[Presentation] 指数型不定方程式 a^x + 3b^y = c^z について2016
- Author(s)
  寺井伸浩
- Organizer
  第135回日本数学会九州支部例会
- Place of Presentation
  長崎大学(長崎県長崎市)
- Year and Date
  2016-10-22
- Data Source
  KAKENHI-PROJECT-15K04786
[Presentation] 指数型不定方程式 a^x+b^y=c^z の解の個数について2016
- Author(s)
  寺井伸浩
- Organizer
  愛知数論セミナー
- Place of Presentation
  愛知工業大学本山キャンパス(愛知県名古屋市)
- Year and Date
  2016-05-21
- Data Source
  KAKENHI-PROJECT-15K04786
[Presentation] Euler商に関する指数型不定方程式について2016
- Author(s)
  寺井伸浩
- Organizer
  第10回福岡数論研究集会
- Place of Presentation
  九州大学伊都キャンパス(福岡県福岡市)
- Year and Date
  2016-08-09
- Data Source
  KAKENHI-PROJECT-15K04786
[Presentation] 指数型不定方程式 (pm^2+1)^x+(qm^2-1)^y=(rm)^z について2015
- Author(s)
  寺井伸浩
- Organizer
  早稲田大学整数論セミナー
- Place of Presentation
  早稲田大学西早稲田キャンパス (東京都新宿区)
- Year and Date
  2015-05-15
- Data Source
  KAKENHI-PROJECT-15K04786
[Presentation] 指数型不定方程式 a^x+b^y=c^z について2015
- Author(s)
  寺井伸浩
- Organizer
  北陸数論セミナー
- Place of Presentation
  金沢大学サテライトプラザ (石川県金沢市)
- Year and Date
  2015-09-17
- Data Source
  KAKENHI-PROJECT-15K04786
[Presentation] 指数型不定方程式に関する Jesmanowicz 予想の一般化について2015
- Author(s)
  寺井伸浩
- Organizer
  第133回日本数学会九州支部例会
- Place of Presentation
  佐賀大学理工学部 (佐賀県佐賀市)
- Year and Date
  2015-10-24
- Data Source
  KAKENHI-PROJECT-15K04786
[Presentation] 楕円曲線y^2=x^3-p^kxの整数点とMordell-Weilランクについて2009
- Author(s)
  寺井伸浩
- Organizer
  早稲田大学整数論セミナー
- Place of Presentation
  早稲田大学大久保キャンパス
- Year and Date
  2009-10-16
- Data Source
  KAKENHI-PROJECT-20540004

1. NAKAMURA Tetsuo (90016147)

# of Collaborated Projects: 1 results

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2. SATO Atsusi (30241516)

# of Collaborated Projects: 1 results

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3. FUJITA Yasutsugu (50514163)

# of Collaborated Projects: 1 results

# of Collaborated Products: 1 results
4. 太刀川弘幸 (20015473)

# of Collaborated Projects: 1 results

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5. 森下和彦 (10254905)

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6. 井上弘 (50146148)

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7. 川島俊雄 (60129020)

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8. 宇内泰 (60048907)

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9. NARA Tadahisa

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10. 宮崎隆史

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Terai Nobuhiro 寺井 伸浩

TERAI Nobuhiro 寺井 伸浩

寺井 伸浩 テライ ノブヒロ

Research Projects

Research Products

Co-Researchers

Study on the generalized Ramanujan-Nagell equationsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Study on exponential Diophantine equations related to Jesmanowicz' conjecturePrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Study on integer solutions of exponential Diophantine equationsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Rational points and integer points on elliptic curves and the related Diophantine equations

Principal Investigator

Project Period (FY)

Research Category

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Research Institution

Complex multiplication of elliptic curves and abelian varieties

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

多元環の表現論および関連する分野の研究

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] A note on the ternary purely exponential Diophantine equation f^x+(f+g)^y=g^z2023

Author(s)

Journal Title

DOI

Data Source

[Journal Article] A note on the solution to the generalized Ramanujan-Nagell equation x^2 + (4c)^y = (c + 1)^z2023

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Journal Title

DOI

Data Source

[Journal Article] A note on the number of solutions of ternary purely exponential Diophantine equations2023

Author(s)

Journal Title

DOI

Data Source

[Journal Article] On the generalized Ramanujan-Nagell equation x^2+b^m=c^n with a^2+b^r=c^22022

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Data Source

[Journal Article] On the generalized Ramanujan-Nagell equation x^2 + (4c)^m = (c + 1)^n2022

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Data Source

[Journal Article] Some exponential Diophantine equations attached to Pythagorean triples2022

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[Journal Article] On exponential Diophantine equations concerning Pythagorean triples2022

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[Journal Article] On the Diophantine equation x^2 + b^m = c^n with a^2 + b^4 = c^22022

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Terai Nobuhiro 寺井伸浩

TERAI Nobuhiro 寺井伸浩

寺井伸浩テライノブヒロ