A guide to elementary number theory / Underwood Dudley [E-Book]
Dudley, Underwood.
[Washington, D.C.] : Mathematical Association of America, c2009
x, 141 pages : illustrations
englisch
Dolciani mathematical expositions ; no. 41
MAA guides ; no. 5
Full Text
Table of Contents:
  • Greatest common divisors
  • Unique factorization
  • Linear Diophantine equations
  • Congruences
  • Linear congruences
  • The Chinese remainder theorem
  • Fermat's theorem
  • Wilson's theorem
  • The number of divisors of an integer
  • The sum of the divisors of an integer
  • Amicable numbers
  • Perfect numbers
  • Euler's theorem and function
  • Primitive roots and orders
  • Decimals
  • Quadratic congruences
  • Gauss's lemma
  • The quadratic reciprocity theorem
  • The Jacobi symbol
  • Pythagorean triangles
  • x⁴ + y⁴ [not equal] z⁴
  • Sums of two squares
  • Sums of three squares
  • Sums of four squares
  • Waring's problem
  • Pell's equation
  • Continued fractions
  • Multigrades
  • Carmichael numbers
  • Sophie Germain primes
  • The group of multiplicative functions
  • Bounds for [pi](x)
  • The sum of the reciprocals of the primes
  • The Riemann hypothesis
  • The prime number theorem
  • The abc conjecture
  • Factorization and testing for primes
  • Algebraic and transcendental numbers
  • Unsolved problems.