| 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)
|
|---|
| 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.
|
