A guide to elementary number theory / Underwood Dudley.
"A Guide to Elementary Number Theory is a 140-page exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in nu...
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| Year of Publication: | 2009 |
| Language: | English |
| Series: | Dolciani mathematical expositions ;
no. 41 MAA guides ; no. 5 |
| Online Access: | |
| Physical Description: | x, 141 p. :; ill. |
| Notes: | Includes index. |
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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.