初等数论 英语
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初等数论 英语
Elementary number theory studies the properties and relations of integers. It
is an important branch of number theory and a basic course in mathematics. The content
of this course includes Euclid's algorithm and unique factorization, congruence,
the Chinese remainder theorem, Euler function, Fermat-Euler's theorem, Wilson
theorem, primitive roots, quadratic reciprocity, factorization of large integers,
the basic version of the RSA encryption method, quadratic rings and Euclidean domain,
sums of two squares revisited, Pell's equation, continued fractions, and sums of
four squares. The purpose of this course is to enable students to understand the
basic ideas in elementary number theory and how more general algebraic theories are
derived from the study of number theory problems, and to understand the application
of number theory in modern information technology.