Fermat's Last Theorem is one of the most famous theorems in mathematics, which states that no three positive integers (a), (b), and (c) can satisfy the equation (a^n + b^n = c^n) for any integer value of (n) greater than 2.
Brief History
The theorem was first proposed by Pierre de Fermat in 1637, and it remained unsolved for over 350 years. Many mathematicians have worked on this problem over the centuries, including Euler, Euler, Lagrange, Gauss, and many others.
Proof
In 1994, Andrew Wiles finally provided a proof of Fermat's Last Theorem. His proof was based on elliptic curves and modular forms, which are advanced topics in mathematics.
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Fermat's Last Theorem and Elliptic Curves
One of the key ingredients in Wiles' proof is the connection between Fermat's Last Theorem and elliptic curves. Elliptic curves are a type of algebraic curve defined by an equation of the form (y^2 = x^3 + ax + b).
Fermat's Last Theorem and Modular Forms
Another key ingredient in Wiles' proof is the connection between Fermat's Last Theorem and modular forms. Modular forms are functions that satisfy certain symmetry properties and are defined on the complex upper half-plane.
Conclusion
Fermat's Last Theorem is a remarkable example of how mathematics can evolve over time. It was a problem that stood for centuries, and it was eventually solved using advanced techniques from various branches of mathematics. For more information on this fascinating topic, please visit our mathematics section.