1. Pythagoras & Fermat
نویسنده
چکیده
This problem is a computational investigation of Pythagoras' Theorem and Fermat's Last Theorem. It involves a branch of number theory known as Diophantine problems after Diophantus of Alexandria, who is thought to have lived around AD 250 and was the first mathematician to write comprehensively about number theory. For non-technical and historical background see the "popular science" book [1] and for mathematical background see, for example, [2]. A Diophantine problem is one that requires whole number or integer solutions. The general problem we will consider is to find all integer solutions for , , x y z of the equation = + x y z for arbitrary positive integer values of n. The problem is trivially solvable for = n 1: any two integer values of x and y and their sum z obviously satisfy the equation. For = n 2 the problem relates to Pythagoras' Theorem and for < 2 n to Fermat's Last Theorem.
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