OEF finite field
--- Introduction ---
This module actually contains 21 exercises on finite fields.
Arithmetics over F4
We designate the 4 elements of the field K=F4 by 0,1,2,3, where 0 and 1 are the respective neutral elements of the additive and multiplicative groups of K. What is the element in K ?
Primitive counting
Compute the number of primitive elements in the finite field K=F. Recall. A non-zero element x in K is primitive, if x is a generator of the multiplicative group of K.
Element power
Compute the element in the finite field K=F.
Inverses in F11
What is the inverse of the element of the field F11? Give your reply by an integer between 0 et 10.
Inverses in F13
What is the inverse of the element of the field F13? Give your reply by an integer between 0 et 12.
Inverses in F17
What is the inverse of the element of the field F17? Give your reply by an integer between 0 et 16.
Inverses in F19
What is the inverse of the element of the field F19? Give your reply by an integer between 0 et 18.
Inverses in F5
What is the inverse of the element of the field F5? Give your reply by an integer between 0 et 4.
Inverses in F7
What is the inverse of the element of the field F7? Give your reply by an integer between 0 et 6.
Element order over F11
What is the multiplicative order of the element of the field F11 ?
Element order over F13
What is the multiplicative order of the element of the field F13 ?
Element order over F16
Let x be an element of the field F16 such that =0. What is the multiplicative order of x?
Element order over F17
What is the multiplicative order of the element of the field F17 ?
Element order over F19
What is the multiplicative order of the element of the field F19 ?
Element order over F25
Let x be an element of the field F25 such that =0. What is the multiplicative order of x?
Element order over F27
Let x be an element of the field F27 such that =0. What is the multiplicative order of x?
Element order over F7
What is the multiplicative order of the element of the field F7 ?
Element order over F9
Let x be an element of the field F9 such that =0. What is the multiplicative order of x?
Primitive power over F16
The polynomial P(x)= is irreducible and primitive over F2, therefore if r is a root of P(x) in the field K=F16, any non-zero element s of K can be written as s=rn for a certain power n. What is the n such that = rn ? (Give your answer by an n between 1 and 15.)
Primitive power over F8
The polynomial P(x)= is irreducible and primitive over F2, therefore if r is a root of P(x) in the field K=F8, any non-zero element s of K can be written as s=rn for a certain power n. What is the n such that = rn ? (Give your answer by an n between 1 and 7.)
Primitive power over F9
The polynomial P(x)= is irreducible and primitive over F3, therefore if r is a root of P(x) in the field K=F9, any non-zero element s of K can be written as s=rn for a certain power n. What is the n such that = rn ? (Give your answer by an n between 1 and 8.)
The most recent version
This page is not in its usual appearance because WIMS is unable to recognize your
web browser.
Please take note that WIMS pages are interactively generated; they are not ordinary
HTML files. They must be used interactively ONLINE. It is useless
for you to gather them through a robot program.
- Description: collection of exercises on finite fields. interactive exercises, online calculators and plotters, mathematical recreation and games
- Keywords: interactive mathematics, interactive math, server side interactivity, algebra, finite field, cyclic group, primitive element, primitive polynomial