Harold M. Edwards is Emeritus Professor of Mathematics at New York University.
Introduction to Number Theory
Numbers The problem $A\square + B = \square$ Congruences
Double congruences and the Euclidean algorithm
The augmented Euclidean algorithm
Simultaneous congruences
The fundamental theorem of arithmetic
Exponentiation and orders
Euler's $\phi$-function
Finding the order of $a\bmod c$ Primality testing
The RSA cipher system
Primitive roots $\bmod\ p$
Polynomials Tables of indices $\bmod\ p$
Brahmagupta's formula and hypernumbers
Modules of hypernumbers
A canonical form for modules of hypernumbers
Solution of $A\square + B = \square$
Proof of the theorem of Chapter 19
Euler's remarkable discovery
Stable modules
Equivalence of modules
Signatures of equivalence classes
The main theorem
Which modules become principal when squared?
The possible signatures for certain values of $A$
The law of quadratic reciprocity
Proof of the Main Theorem
The theory of binary quadratic forms
Composition of binary quadratic forms
Cycles of stable modules
Answers to exercises
Bibliography
Index
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