The Frey-Ribet Theorem is a significant result in number theory that connects the properties of certain elliptic curves to the solution of Diophantine equations, specifically Fermat's Last Theorem. This theorem shows that if a specific type of elliptic curve can be associated with a supposed solution to Fermat's equation, then this elliptic curve must have unusual properties, which leads to a contradiction. The connection between elliptic curves and number theory underscores the importance of elliptic functions and the Weierstrass ℘-function in understanding the theorem's implications.
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