## Description

Divisibility Theory in Integers : Introduction, Division Algorithm, Greatest Common Divisor, Least Common Multiple, The Diophantine Equation a x + b y = c,

Primes and Their Distribution : The Fundamental Theorem of Arithmetic, The Sieve of Eratiosthenes, The Goldbach Conjecture

Theory of Congruences : Basic Properties of Congruences, Special Divisibility Tests, Linear Congruences

Fermat’s Theorem : Fermat’s Factorization Method, The Little Theorem, Wilson’s Theorem

Number-Theoretic Functions : The Functions t and s, The Mobius Inversion Formula, The Greatest Integer Function

Euler’s Generalization of Fermat’s Theorem : Euler’s Phi-Function, Euler’s Theorem, Some Properties of Euler’s Phi Function, An Application of Cryptography

Primitive Roots and Indices : Order of an Integer Modulo n, Primitive Roots for Primes, Composite Numbers having Primitive Roots, The Theory of Indices

The Quadratic Reciprocity Law : Euler’s Criterion, The Legendre Symbol and its Properties, Quadratic Reciprocity, Quadratic Congruences with Composite Moduli, The Jacobi Symbol

Number of Special Form : Perfect Numbers, Mersenne Primes and Amicable Numbers, Fermat Number

Binary Quadratic Forms : Binary Quadratic Forms, Equivalence and Reduction of Binary Quadratic Forms, Positive Definite Binary Quadratic Forms

Sum of Squares of Integers : Sum of Two Squares, Difference of Two Squares, Sum of Three or Four Squares

Some Non-Linear Diophantine Equations : Pythagorean Triangles, Fermat’s Last Theorem, Miscellaneous Problems