More than 370 years ago the famous French mathematician Pierre de Fermat proposed to solve the following problem: to find a Pythagorean triples whose hypotenuse and the sum of the legs were squares, which, despite its simplicity, has been very difficult. Problems associated with its solution involved many mathematicians such as (Leonhard Euler, Joseph-Louis Lagrange, Ljnggren, Wacław Sierpiński and etc.) But in the end it did not reach solution. In our article, solution communicated to obtain the equations giving the required values all elements of the Pythagorean triples in positive integers (natural) are co-prime integers, and provides a second solution of thisproblem (the values of x, y, z of 45 digits), and some consequences.

Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 7)

Pages:

46-53

Citation:

K. R. R. Gandhi and R. Tint, "The Pythagorean Triples Whose Hypotenuse and the Sums of the Legs are Squares", The Bulletin of Society for Mathematical Services and Standards, Vol. 7, pp. 46-53, 2013

Online since:

September 2013

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

Diophantus of Alexandria Arithmetica, Наука, Главная редакция физико- математической литературы, Москва, (1974).

W. Sierpiński, Пифагоровы треугольники, Государственное учебно- педагогическое издательство, Москва, (1959).

W. Sierpiński, 250 задач по элементарной теории чисел", "Просвещение, Москва, (1968).

W. Sierpiński, О решении уравнений в целых числах, Физматгиз, Москва (1961).

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