This PDF covers the
following topics related to Number Theory : Divisibility, Prime Numbers, The
Linear Diophantine Equation , Congruences, Linear Congruences, The Chinese
Remainder Theorem, Public-Key Cryptography, Pseudoprimes, Polynomial
Congruences with Prime Moduli, Polynomial Congruences with Prime Power
Moduli, The Congruence, General Quadratic Congruences, The Legendre Symbol
and Gauss’ Lemma, Quadratic Reciprocity, Primitive Roots, Arithmetic
Functions, Sums of Squares, Pythagorean Triples, Fermat’s Last Theorem,
Continued Fractions, Simple Continued Fractions, Rational Approximations to
Irrational Numbers, Periodic Continued Fractions, Continued Fraction
Expansion, Pell’s Equation.
This PDF covers the
following topics related to Number Theory : Divisibility, Prime Numbers, The
Linear Diophantine Equation , Congruences, Linear Congruences, The Chinese
Remainder Theorem, Public-Key Cryptography, Pseudoprimes, Polynomial
Congruences with Prime Moduli, Polynomial Congruences with Prime Power
Moduli, The Congruence, General Quadratic Congruences, The Legendre Symbol
and Gauss’ Lemma, Quadratic Reciprocity, Primitive Roots, Arithmetic
Functions, Sums of Squares, Pythagorean Triples, Fermat’s Last Theorem,
Continued Fractions, Simple Continued Fractions, Rational Approximations to
Irrational Numbers, Periodic Continued Fractions, Continued Fraction
Expansion, Pell’s Equation.
This note covers the following topics: Primes in
Arithmetic Progressions, Infinite products, Partial summation and Dirichlet
series, Dirichlet characters, L(1, x) and class numbers, The distribution of the
primes, The prime number theorem, The functional equation, The prime number
theorem for Arithmetic Progressions, Siegel’s Theorem, The Polya-Vinogradov
Inequality, Sums of three primes, The Large Sieve, Bombieri’s Theorem.
Robert Daniel Carmichael (March
1, 1879 – May 2, 1967) was a leading American mathematician.The purpose of this
little book is to give the reader a convenient introduction to the theory of
numbers, one of the most extensive and most elegant disciplines in the whole
body of mathematics. The arrangement of the material is as follows: The five
chapters are devoted to the development of those elements which are essential to
any study of the subject. The sixth and last chapter is intended to give the
reader some indication of the direction of further study with a brief account of
the nature of the material in each of the topics suggested.
This
note explains the following topics:
Algebraic numbers, Finite continued fractions, Infinite continued fractions,
Periodic continued fractions, Lagrange and Pell, Euler’s totient function,
Quadratic residues and non-residues, Sums of squares and Quadratic forms.