OEF modular arithmetic --- Introduction ---

This module actually contains 38 exercises on computations in the finite ring Z/nZ.

Addition fill

, . , .

Congruence classes

?

Congruences with a parameter

.
0 .

Cubic fill

, . , .

Division fill

, . , .

Division I

/ .
0 .

Division II

/ .
0 .

Division III

/ .
0 .

Zero divisors

?

Zero divisor II

.
. 1 ,

Zero divisors III

=2, . ?

Roots modulo p^2

. . .
0 .

ZZ.

.

0 .

.

,
.
0 ,

?

: .

0 , .

( ) ?

Inverse I

.
0 .

Inverse II

.
1 .

Inverse III

.
0 .

Invertible power

. . ?

Divisibility

. ?

Linear modular equation

equiv
?
A + M . . A + . .
 +

Multiplication fill

, . , .

Special multiples

.

Special multiples II

. .

Period of a decimal in base b

. ?

Polynomial fill

, . , .

Powers

.
0 .

Powers II

. .
0 .

Power fill

, . , .

Roots modulo p

equiv .

Roots

. , . .
.

Roots of unity modulo p (I)

equiv 1 .
equiv 1

Roots of unity modulo p (II)

equiv 1 .

Simple computations in Z/nZ

.
0 .

Simple computations modulo n

.
0 .

Squares

.
0 ,

Sum and product

,

,

,


Linear system modulo n II

= * + *
= * + *
.

Linear system modulo n I


Linear system modulo n II

= + * + *
= + * + *
.

Trinomial fill

, . , .

Other exercises on: Modular arithmetic  


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Description: collection of exercises on the ring Z/nZ. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games

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