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Все авторы >> Пойа Дж.

He was born as Gy&246;rgy Pólya in Budapest, Hungary, and died in Palo Alto, USA. For most of his career in the United States, he was a professor of mathematics at Stanford University. He worked on a great variety of mathematical topics, including series, number theory, combinatorics, and probability. In his later days, he spent considerable effort on trying to characterize the methods that people use to solve problems, and to describe how problem-solving should be taught and learned. He wrote three books on the subject: How to Solve It, Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics, and Mathematics and Plausible Reasoning Volume II: Patterns of Plausible Reasoning. In How to Solve It, Pólya provides general heuristics for solving problems of all kinds, not only mathematical ones. The book includes advice for teaching students of mathematics and a mini-encyclopedia of heuristic terms. It was translated into several languages and has sold over a million copies. Russian physicist Zhores I. Alfyorov, (Nobel laureate in 2000) praised it, saying he was very pleased with Pólya's famous book. The book is still referred to in mathematical education. Douglas Lenat's Automated Mathematician and Eurisko artificial intelligence programs were inspired by Pólya's work. In 1976 The Mathematical Association of America established the George Pólya award "for articles of expository excellence published in the College Mathematics Journal."

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Задача 73702

Темы:   [ Теорема Эйлера ]
[ Арифметическая прогрессия ]
[ Простые числа и их свойства ]
[ Разложение на множители ]
Сложность: 4
Классы: 8,9,10

Автор: Пойа Дж.

В любой арифметической прогрессии  a,  a + d,  a + 2d,  ...,  a + nd,  ...,  составленной из натуральных чисел, есть бесконечно много членов, в разложении которых на простые множители входят в точности одни и те же простые числа. Докажите это.

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Проект осуществляется при поддержке Департамента образования г.Москвы и ФЦП "Кадры" .