STNB2026 (39th edition)
Revisiting the Fermat equation of exponents (3,3,p)
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Diana Mocanu
Resumen
Wiles’ famous proof of Fermat’s Last Theorem opened up the possibility of tackling many Diophantine equations using the same method, called the modular method. In this talk, I will give a brief sketch of the modular method and then use it to show that the equation $x^3+y^3=5^\alpha c^p$ has no non-trivial coprime solutions for p in a given list of primes. In the elimination step, I will use a recent joint work with Nuno Freitas on local points on twists of the modular curve X(p).
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