Number Theory
These are notes on elementary number theory; that is, the part of number theory which does not involves methods from abstract algebra or complex variables.The first link in each item is to a Web page; the second is to a PDF (Adobe Acrobat) file. Use the PDF if you want to print it.
These notes have been revised at various times, some in 2008 and some in 2011.
- The ring of integers. [PDF]
- Induction. [PDF]
- Sums, products, and factorials. [PDF]
- Divisibility and the Division Algorithm. [PDF]
- Prime numbers. [PDF]
- Greatest common divisors. [PDF]
- The Extended Euclidean Algorithm. [PDF]
- The Fundamental Theorem of Arithmetic. [PDF]
- Elementary factoring methods; Fermat factorization. [PDF]
- Linear Diophantine equations. [PDF]
- Congruences and modular arithmetic. [PDF]
- Solving linear congruences (one and two variables). [PDF]
- The Chinese Remainder Theorem. [PDF]
- Systems of linear congruences. [PDF]
- Wilson's Theorem and Fermat's Theorem. [PDF]
- Euler's Theorem; the Euler phi function. [PDF]
- Properties of the Euler phi function; multiplicative functions; Dirichlet products; Möbius inversion. [PDF]
- The sum and number of divisors functions. [PDF]
- Perfect numbers and Mersenne primes. [PDF]
- Character and block ciphers. [PDF]
- Exponential ciphers; the RSA algorithm. [PDF]
- Quadratic residues. [PDF]
- Quadratic reciprocity. [PDF]
- Decimal and base-b fractions. [PDF]
- Finite continued fractions. [PDF]
- Infinite continued fractions. [PDF]
- Periodic continued fractions. [PDF]
- Approximation by rationals. [PDF]
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