Acharya, Bhaskara , 93 , 197
algebraic integer , 109
algebraic numbe r theory , 109
algorithm
augmented Euclidean , 24-2 6
comparison, 9 3
division wit h remainder , 4 , 5
Euclidean, 19, 182
exponentiation, 3 7
factorization, 53 , 5 4
Miller's test , 53 , 189
multiplication, 2 , 3
reduction, 104
Archimedes, 8 , 9
augmented Euclidea n algorithm ,
23-26, 59 , 6 4
binary quadrati c form , xii , 155-160
Brahmagupta, 77 , 93 , 9 7
Brahmagupta's formula , 77-79 , 163
canonical form , 87-9 1
Chinese remainde r theorem , 3 0
class group , 127
comparison algorithm , 9 3
composite number , 3 3
composition o f forms , 163-16 7
congruence, 11-1 3
congruence o f hypernumbers , 81-83
conjugate o f a module , 102
content o f a module , 102
counting, 1-5
cube roo t mo d p , 7 3
Dirichlet, G . Lejeune , 115
discriminant o f a form , 156
Disquisitiones Arithmeticae , ix-xii ,
11, 62 , 163
division, 4
division b y a mo d 6 , 2 7
division wit h remainder , 4 , 6 8
double congruence , 18
equality o f modules , 8 1
equivalence o f forms , 157
equivalence o f modules , 123, 124
Euclidean algorithm , 18, 24 , 8 2
Euler's criterion , 114
Euler's generalizatio n o f Fermat' s
theorem, 4 8
Euler's law , 116, 129, 136, 154
Euler, Leonhard , xi , 43 , 114-116
exponentiation, 37-3 9
Farey series , 2 7
Fermat's theorem , 48 , 51, 6 3
form, see binar y quadrati c for m
fundamental theore m o f arithmetic ,
33, 3 4
fundamental unit , 108, 109
209
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