2017 Fiscal Year Final Research Report
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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| 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 |
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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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| Free Research Field |
整数論
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