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Can some one show me how to do multiplication over gf(16) step by step

I cannot determine how many solutions are in x^15 - 1

Tamerlantame
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  • To get a bit of experience with multiplications in this field you may want to take a look at this Q&A pair I prepared with referrals like this in mind. As Bernard explained, you don't need that to be able to answer the question, but for some other tasks it may be necessary. – Jyrki Lahtonen Nov 22 '20 at 15:07
  • I'm fairly sure we have handled essentially the same question before, but I don't have time to look for it now. That's why I won't upvote Bernard's answer. – Jyrki Lahtonen Nov 22 '20 at 15:08

1 Answers1

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You don't have to know the multiplication table in $\mathbf F_{16}$: the multiplicative group $\mathbf F_{16}^\times$ has order $15$, hence by Lagrange's theorem, each element in this group has order a divisor of $15$.

Bernard
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