## Number Theory## and Its History## Oystein Ore## CONTENTSPreface
- Numbers and counting
- Basic number groups
- The number systems
- Large numbers
- Finger numbers
- Recordings of numbers
- Writing of numbers
- Calculations
- Positional numeral systems
- Hindu-Arabic numerak
- Number theory and numerology
- Multiples and divisors
- Division and remainders
- Number systems
- Bimu number systems
- Greatest conunon divisor. Euclid's algorism
- The division lemma
- Umt common multiple
- Greatest common divisor and least common multiple for several numbers
- Prime numbers and the prime factorization theorem
- Determination of prime factors
- Factor tables
- Fermat's factorization method
- Euler's factorization method
- The sieve of Eratosthenes
- Mersenne and Fermat primes
- The distribution of primes
- The divisors of a number
- Perfect numbers
- Amicable numbers
- Greatest common divisor anl least common multiple
- Euler's function
- Problems and puzzles
- Indeterminate problems
- Problems with two unknowns
- Problems with several unknowns
- Theory of linear indeterminate equations with two unknowns
- Linear indeterminate equations in several unknowns
- Classification of systems of numbers
- The Pythagorean triangle
- The Plimpton Library tablet
- Diophantos of Alexandria
- Al-Karkhi and Leonardo Pisano
- From Diophantos to Fermat
- The method of infinite descent
- Fermat's last theorem
- The Disquisitiones arithmeticae
- The properties of congruences
- Residue systems
- Operations with congruences
- Casting out nines
- Algebraic congruences
- Linear congruences
- Simultaneous congruences and the Chinese remainder theorem
- Further study of algebraic congruences
- Wilson's theorem
- Gauss's generalization of Wilson's theorem
- Representations of numbers as the sum of two squares
- Euler's theorem
- Fermat's theorem
- Exponents of numbers
- Primitive roots for primes
- Primitive roots for powers of primes
- Universal exponents
- Indices
- Number theory and the splicing of telephone cables
- Decimal fractions
- The properties of decimal fractions
- The converse of Fermat's theorem
- Numbers with the Fermat property
- The classical construction problems
- The construction of regular polygons
- Examples of constructible polygons
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