Study on integer solutions of exponential Diophantine equations
| Project/Area Number |
15K04786
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Oita University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 指数型不定方程式 / 整数解 / Jesmanowicz予想 / Terai予想 / Baker理論 / 一般化されたFermat方程式 / 楕円曲線 / 数論 / 不定方程式 |
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| Outline of Final Research Achievements |
Our purpose of this research is to determine integer solutions of exponential Diophantine equations (1) a＾x + b＾y = c＾z, (2) (pm＾2 + 1)＾x + (qm＾2 - 1)＾y = (rm)＾z with p+q=r＾2 (3) (a＾φ(m)-1)/m = x＾l, where φ is Euler's totient function, under some conditions. Our method is based on elementary methods, Baker's method and deep results on generalized Fermat equations via sophisticated arguments in the theory of elliptic curves and modular forms.
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Report
(4 results)
Research Products
(17 results)
