preface
introduction
1 what is number theory?
2 pythagorean triples
3 pythagorean triples and the unit circle
4 sums of higher powers and fermat s last theorem
5 divisibility and the greatest common divisor
6 linear equations and the greatest common divisor
7 factorization and the fundamental theorem of aritrhmetic
8 congruences
9 congruences,powers,and fermat s little theorem
10 congruences,poers,and euler s formula
11 euler s phi function and the chinese remainder theorem
12 prime numbers
13 counting primes
14 mersenne primes
15 mersenne primes and perfect numbers
16 powers modulo m and successive squaring
17 computiong kth roots modulo m
18 powers,roots,and“unbreakable”codes
19 primality testing and carmichael numbers
20 euler s phi function and sums of divisros
21 powers modulo p and primitive roots
22 primitive roots and indices
23 squares modulo p
24 is-l a square modulo p?is 2?
25 quadratic reciprocity
26 which primes are sums of two squares?
27 which unmbers are sums of two squares?
28 the equation x4+y4=z4
29 square-triangular numbers revisited
30 rell s equation
31 diophantine approximation
32 diophantine approximation and pell s equation
33 number theory and imaginary numbers
34 the gaussian integers and unique factorization
35 irrational numbers and transcendental numbers
36 binomial coefficients and pascal s triangle
37 fibonacci s rabbits and linear recurrence sequences
38 oh,what a beautiful function
39 the topsy-turvy world of continued fractions
40 continued fractions,square roots,and pell s equation
41 continued fracte roots,and pell s equation
42 sums of powers
43 cubic curves and elliptic curves
44 elliptic curves with few rational points
45 points on elliptic curves modulo p
46 torsion collections modulo pand bad primes
47 defect bounds and modularity patterns
48 elliptic curves and fermat s last theorem
A factorization of small composite integers
B a list of primes
index
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