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The entire subject matter in the present book has been arranged in a simple, systematic, graded, lucid and exhaustive manner. Each chapter begins with definitions followed by theorems with complete proofs and solved problems. A large number of notes and remarks have been added for better understanding of the subject. For UGC-CSIR NET examination, some MCQ’s from the previous years papers and other similar questions have been added at the end of the book.


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

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