Number Theory : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

Elementary number theory is discussed in this chapter. Sets, functions, and basic number-theoretic topics like countability, divisibility, prime numbers, greatest common divisor, and continued fractions are defined and discussed in this chapter. Basics of congruence arithmetic, Chinese remainder theorem, Moebius function, Euler’s phi-function, modular arithmetic, quadratic residues, and Legendre and Jacobi symbols are also examined. Properties of cyclotomic polynomials are also stated. Finally, certain useful combinatorial results are outlined. Some of these topics are explained in terms of matrices, polynomials, and basic group theory. The reader who is not familiar with these terms and concepts is urged to refer to the appropriate chapters.