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SOURCE:   Almanac of Modern Science and Education. Tambov: Gramota, 2015. № 10. P. 110-113. ISSN 1993-5552.
SCIENTIFIC AREA: Physical-Mathematical Sciences
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GENERAL SOLUTION OF FERMAT QUADRATIC EQUATION AND ITS CONNECTION WITH PRIME NUMBERS

Romanov Vadim Nikolaevich
Saint Petersburg


Abstract. The article provides a general solution of Fermat quadratic equation, analyzes the behaviour of different classes of the basic solutions of the equation. The author shows the possibility to use the solutions for generating prime numbers and proving Landau’s hypothesis and Goldbach’s binary hypothesis. The theoretical studies are followed by the examples clarifying the general correlations.
Key words and phrases: теория чисел, теорема Ферма, натуральные числа, общее решение квадратного уравнения Ферма, генерация простых чисел, бинарная гипотеза Гольдбаха, гипотеза Ландау, theory of numbers, Fermat theorem, natural numbers, general solution of Fermat quadratic equation, prime numbers generation, Goldbach’s binary hypothesis, Landau’s hypothesis.
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References:
  1. Romanov V. N. O reshenii binarnoi problemy Gol'dbakha // Al'manakh sovremennoi nauki i obrazovaniya. Tambov: Gramota, 2014. № 12 (90). C. 95-100.
  2. Romanov V. N. Ob odnom sposobe dokazatel'stva teoremy Ferma // Al'manakh sovremennoi nauki i obrazovaniya. Tambov: Gramota, 2014. № 3 (82). C. 139-143.

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