Prove that the polynomial x^2 + x + 1 is irreducible over
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Prove that the polynomial x^2 + x + 1 is irreducible over F , the field of integers modulo 2.
The complete problem is in the attached file.
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Solution Summary
It proves that the polynomial x^2 + x + 1 is irreducible over F , the field of integers modulo 2.
It also defines the two operations addition modulo 2 and multiplication modulo 2 of the field of
integers F.
The solution is given in detail.
Solution Preview
The solution is in the attached file.
Algebra (II)
By:- Thokchom Sarojkumar Sinha
Prove that the polynomial
is irreducible over F, the field of integers modulo 2.
Solution:- Let
Also let F be the field of integers modulo 2,
then F = { 0,1} where the operations of F are addition modulo 2
and multiplication modulo 2
or,
We have ,
where
Therefore
...
Education
- BSc, Manipur University
- MSc, Kanpur University
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