Geodesic
On a Few Diophantine Equations Related to Fermat’s Last Theorem
Canadian mathematical bulletin, Tome 45 (2002) no. 2, pp. 247-256

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DOI

We combine the deep methods of Frey, Ribet, Serre and Wiles with some results of Darmon, Merel and Poonen to solve certain explicit diophantine equations. In particular, we prove that the area of a primitive Pythagorean triangle is never a perfect power, and that each of the equations ${{X}^{4}}\,-\,4{{Y}^{4}}\,=\,{{Z}^{p}},\,{{X}^{4}}\,+\,4{{Y}^{p}}\,=\,{{Z}^{2}}$ has no non-trivial solution. Proofs are short and rest heavily on results whose proofs required Wiles’ deep machinery.
DOI : 10.4153/CMB-2002-028-1
Mots-clés : 11D41, Diophantine equations 
Kihel, O.; Levesque, C. On a Few Diophantine Equations Related to Fermat’s Last Theorem. Canadian mathematical bulletin, Tome 45 (2002) no. 2, pp. 247-256. doi: 10.4153/CMB-2002-028-1
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     title = {On a {Few} {Diophantine} {Equations} {Related} to {Fermat{\textquoteright}s} {Last} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {247--256},
     year = {2002},
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     doi = {10.4153/CMB-2002-028-1},
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