On a Few Diophantine Equations Related to Fermat's Last Theorem

Canadian mathematical bulletin

关键词: Diophantine equations;   

DOI  :  10.4153/CMB-2002-028-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We combine the deep methods of Frey, Ribet, Serre and Wiles with someresults of Darmon, Merel and Poonen to solve certain explicitdiophantine equations. In particular, we prove that the area of aprimitive Pythagorean triangle is never a perfect power, and that eachof the equations $X^4 - 4Y^4 = Z^p$, $X^4 + 4Y^p = Z^2$ has nonon-trivial solution. Proofs are short and rest heavily on resultswhose proofs required Wiles' deep machinery.

【 授权许可】

Unknown