Elementary Number Theory

Number theory can be used to find the greatest common divisor, determine whether a number is prime, and solve Diophantine equations. With the improvement of computer technology, number theory also helps us to protect private information by encrypting it as it travels through the internet. During the course, we discuss mathematical induction, division and Euclidean algorithms, the Diophantine equation ax + by = c, the fundamental theorem of arithmetic, prime numbers and their distribution, the Goldbach conjecture, congruences, the Chinese remainder theorem, Fermat's theorem, Wilson's theorem, Euler's theorem, and cryptography. Additional topics may include number-theoretic functions, primitive roots, and the quadratic reciprocity law.