What is the inverse of X modulo $1 + X + X^2 + X^3 + X^4$? [duplicate]












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This question already has an answer here:




  • Let $theta$ be a root of $p(x)=x^3+9x+6$, find the inverse of $1+theta$ in $mathbb{Q(theta)}$

    2 answers




What is the inverse of X modulo $1 + X + X^2 + X^3 + X^4$?
Is there any open softwares to calculate such things easily?






ring-theory inverse irreducible-polynomials







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marked as duplicate by Saad, GNUSupporter 8964民主女神 地下教會, jgon, Bill Dubuque ring-theory
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This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.











  • 1




    $begingroup$
    Hint $bmod, 1+xf!:, (-f)xequiv 1 $
    $endgroup$
    – Bill Dubuque
    Dec 4 '18 at 14:40


















-1












$begingroup$



This question already has an answer here:




  • Let $theta$ be a root of $p(x)=x^3+9x+6$, find the inverse of $1+theta$ in $mathbb{Q(theta)}$

    2 answers




What is the inverse of X modulo $1 + X + X^2 + X^3 + X^4$?
Is there any open softwares to calculate such things easily?






ring-theory inverse irreducible-polynomials







share|cite|improve this question











$endgroup$



marked as duplicate by Saad, GNUSupporter 8964民主女神 地下教會, jgon, Bill Dubuque ring-theory
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 Dec 4 '18 at 15:25


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.











  • 1




    $begingroup$
    Hint $bmod, 1+xf!:, (-f)xequiv 1 $
    $endgroup$
    – Bill Dubuque
    Dec 4 '18 at 14:40
















-1












-1








-1





$begingroup$



This question already has an answer here:




  • Let $theta$ be a root of $p(x)=x^3+9x+6$, find the inverse of $1+theta$ in $mathbb{Q(theta)}$

    2 answers




What is the inverse of X modulo $1 + X + X^2 + X^3 + X^4$?
Is there any open softwares to calculate such things easily?






ring-theory inverse irreducible-polynomials







share|cite|improve this question











$endgroup$





This question already has an answer here:




  • Let $theta$ be a root of $p(x)=x^3+9x+6$, find the inverse of $1+theta$ in $mathbb{Q(theta)}$

    2 answers




What is the inverse of X modulo $1 + X + X^2 + X^3 + X^4$?
Is there any open softwares to calculate such things easily?





This question already has an answer here:




  • Let $theta$ be a root of $p(x)=x^3+9x+6$, find the inverse of $1+theta$ in $mathbb{Q(theta)}$

    2 answers







ring-theory inverse irreducible-polynomials




ring-theory inverse irreducible-polynomials






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 4 '18 at 9:26









José Carlos Santos

155k22124227




155k22124227










asked Dec 4 '18 at 9:23









malleamallea

29919




29919




marked as duplicate by Saad, GNUSupporter 8964民主女神 地下教會, jgon, Bill Dubuque ring-theory
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 Dec 4 '18 at 15:25


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marked as duplicate by Saad, GNUSupporter 8964民主女神 地下教會, jgon, Bill Dubuque ring-theory
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 Dec 4 '18 at 15:25


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.










  • 1




    $begingroup$
    Hint $bmod, 1+xf!:, (-f)xequiv 1 $
    $endgroup$
    – Bill Dubuque
    Dec 4 '18 at 14:40
















  • 1




    $begingroup$
    Hint $bmod, 1+xf!:, (-f)xequiv 1 $
    $endgroup$
    – Bill Dubuque
    Dec 4 '18 at 14:40










1




1




$begingroup$
Hint $bmod, 1+xf!:, (-f)xequiv 1 $
$endgroup$
– Bill Dubuque
Dec 4 '18 at 14:40






$begingroup$
Hint $bmod, 1+xf!:, (-f)xequiv 1 $
$endgroup$
– Bill Dubuque
Dec 4 '18 at 14:40












1 Answer
1






active

oldest

votes


















1












$begingroup$

Hint: $1+X+X^2+X^3+X^4=1+X(1+X+X^2+X^3)$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Got it! Thank you very much :)
    $endgroup$
    – mallea
    Dec 4 '18 at 13:33


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









1












$begingroup$

Hint: $1+X+X^2+X^3+X^4=1+X(1+X+X^2+X^3)$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Got it! Thank you very much :)
    $endgroup$
    – mallea
    Dec 4 '18 at 13:33
















1












$begingroup$

Hint: $1+X+X^2+X^3+X^4=1+X(1+X+X^2+X^3)$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Got it! Thank you very much :)
    $endgroup$
    – mallea
    Dec 4 '18 at 13:33














1












1








1





$begingroup$

Hint: $1+X+X^2+X^3+X^4=1+X(1+X+X^2+X^3)$.






share|cite|improve this answer









$endgroup$



Hint: $1+X+X^2+X^3+X^4=1+X(1+X+X^2+X^3)$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 4 '18 at 9:25









José Carlos SantosJosé Carlos Santos

155k22124227




155k22124227












  • $begingroup$
    Got it! Thank you very much :)
    $endgroup$
    – mallea
    Dec 4 '18 at 13:33


















  • $begingroup$
    Got it! Thank you very much :)
    $endgroup$
    – mallea
    Dec 4 '18 at 13:33
















$begingroup$
Got it! Thank you very much :)
$endgroup$
– mallea
Dec 4 '18 at 13:33




$begingroup$
Got it! Thank you very much :)
$endgroup$
– mallea
Dec 4 '18 at 13:33



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