A Pythagorean triple is a set of three positive integers $(a, b, c)$ that satisfy the equation $$a^2 + b^2 = c^2$$, where $c$ is the largest number and represents the hypotenuse of a right triangle. These triples are fundamental in the study of geometry and number theory, illustrating the relationship between the sides of right triangles. They also connect to the concept of irrational numbers when considering the lengths of sides that cannot be expressed as integers.
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