Elementary number theory is a basic course to study the properties of integers. Its main contents include integer divisibility theory, congruence theory, continued fraction theory and some special indefinite equations.
Chapter 1 The divisibility of integer 1, its concept, divisibility with remainder 2, greatest common divisor and division by turns 3, further properties of divisibility and least common multiple 4. Prime number, fundamental theorem of arithmetic 5, function [x, {x} and its application in number theory.
The second chapter introduces indefinite equation 1, binary linear indefinite equation 2, multivariate linear indefinite equation 3, Pythagorean number and Fermat problem.
Chapter 3: congruence 1, concept and basic properties of congruence 2, residue class and complete residue system 3, simplified residue system and Euler function 4, euler theorem, Fermat theorem and its application to cyclic decimals.
Chapter 4 congruence formula 1, basic concepts and first-order congruence formula 2, Sun Tzu's theorem 3, the number of solutions of higher-order congruence formula and its solution method 4, congruence formula of prime number module.
In chapter 5, quadratic congruence and square residue 1, general quadratic congruence 2, square residue and simple prime number square residue 3, Legendre symbol 4, proof of the above theorem 5, Jacobian symbol 6, and the case of composite modules.