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Imperial Library
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Index
Cover page
Halftitle page
Series page
Title page
Copyright page
Contents
List of illustrations
Chapter 1 What is number theory?
Integers
Squares and cubes
Perfect numbers
Prime numbers
Chapter 2 Multiplying and dividing
Multiples and divisors
Least common multiple and greatest common divisor
Euclid’s algorithm
Squares
Divisor tests
Chapter 3 Prime-time mathematics
The sieve of Eratosthenes
Primes go on for ever
Factorizing into primes
Searching for primes
Chapter 4 Congruences, clocks, and calendars
Clock arithmetic
Congruences and the calendar
Solving linear congruences
Chapter 5 More triangles and squares
Linear Diophantine equations
Right-angled triangles
Sums of squares
Higher powers
Chapter 6 From cards to cryptography
Fermat’s little theorem
Generalizing Fermat’s little theorem
Factorizing large numbers
Chapter 7 Conjectures and theorems
Two famous conjectures
The distribution of primes
Primes in arithmetic progressions
Unique factorization
Chapter 8 How to win a million dollars
Infinite series
The zeta function
The Riemann hypothesis
Consequences
Chapter 9 Aftermath
The first ten questions
Integers
Squares and cubes
Perfect numbers
Prime numbers
Further reading
Index
Economics
Information
Innovation
Nothing
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