Название спецкурса на русском языке
Дополнительные главы аналитической теории чисел.
Перевод названия курса на английский язык
Additional Chapters of Analytic Number Theory
Авторы курса
Гриценко Сергей Александрович
Целевая аудитория
2 курс
3 курс
4 курс
5 курс
6 курс
Подразделение
[Кафедра МКМА]
Семестр
Полгода (осень)
Тип курса
Спецкурс на английском языке
Учебный год
2020/21
Аудитория
[Неприменимо]
Аннотация
Elementary properties of integers: divisibility, the unit, prime numbers, the sieve of Eratosthenes, the number of prime is infinite, the fundamental theorem of Euclid, the unique factorization theorem, the greatest common factor of two or more integers, the least common multiple of two or more integers, scales of notation, highest power of a prime contained in a factorial.
Arithmetical functions: the Euler’s totient function, the divisor function, the M\”obius function.
Elementary properties of congruencies: linear congruencies, properties of congruencies relative to division, congruencies with a prime and a prime-power moduli.
The theorems ofFermatand Wilson: Euler’s proof of the simple Fermat theorem, Wilson theorem, the converse of Wilson’s theorem, the converse of the simple Fermat theorem, application preceding results to linear congruencies and to the theory of quadratic residues.
Primitive roots an integer modulo: exponent of an integer modulo, definition of primitive roots, primitive roots a prime modulo, primitive roots a prime-power modulo, primitive roots a twofold prime-power modulo.
Diophatine Analysis: rational triangles, method of infinite descent, problems involving a multiplicative domain, equations of the small degrees, equations of degree higher than fourth, the Fermat problem, the method of functional equations.
Дополнительная информация

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