Algebraic Number Theory
Pythagorean triples are sets of three positive integers $(a, b, c)$ that satisfy the equation $a^2 + b^2 = c^2$. These triples represent the side lengths of a right triangle, with 'c' being the length of the hypotenuse. The existence and properties of Pythagorean triples are key elements in exploring integer solutions to equations related to Fermat's Last Theorem and related problems in number theory.
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