OEF modular arithmetic
--- Introduction ---
This module actually contains 23 exercises on computations in the
finite ring 
/n.
Addition fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Cubic fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Division fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Division I
Compute / in /. The result must be represented by a number between 0 and .
Division II
Compute / in /. The result must be represented by a number between 0 and .
Division III
Compute / in /. The result must be represented by a number between 0 and .
Zero divisors
Is a zero divisor in / ?
Zero divisor II
Find the set of zero divisors in /. (In this exercise we don't consider 0 as a zero divisor.) Write each element by a number between 1 and , and separate the elements by commas.
Zero divisors III
We have =2, where is a prime. How many zero divisors there are in / ? In this exercise we don't consider 0 as a zero divisor.
Inverse I
Find the inverse of in /. The result must be represented by a number between 0 and .
Inverse II
Find the inverse of in /. The result must be represented by a number between 1 and .
Inverse III
Find the inverse of in /. The result must be represented by a number between 0 and .
Invertible power
is a prime. Consider the function f: / -> / defined by f(x)=x . Is f bijective?
Multiplication fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Polynomial fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Powers
Compute the element in /. The result must be represented by a number between 0 and .
Powers II
is a prime number. Compute the element in /. The result must be represented by a number between 0 and .
Power fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Roots
is a prime number. There is an element a in /, such that a is congruent to modulo . Find a. The result must be represented by a number between 0 and .
Simple computations modulo n
Compute in /. The result must be represented by a number between 0 and .
Squares
Find the set of squares in /. (A square in / is an element which is the square of another one.) Write each element by a number between 0 and , and separate the elements by commas.
Sum and product
Find two integers , such that 0 
, 0 , + 
(mod ) , × (mod ) .
You may enter the two numbers in any order.
Trinomial fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
The most recent version
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- Description: collection of exercises on the ring Z/nZ. interactive exercises, online calculators and plotters, mathematical recreation and games
- Keywords: interactive mathematics, interactive math, server side interactivity, algebra, arithmetic, number theory, arithmetic, modular, modulo, congruence