How to eliminate the denominator in the calculation of the Lagrange interpolation on a finite field?

Asked Jan 21 '22 at 02:10

Active Jan 21 '22 at 02:53

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I am studying Secret Sharing by looking at the lecture notes here:

But I could not understand why the following congruence equation holds in the part where the Lagrange interpolation is calculated on a finite field:

\begin{align*} \frac{(x-4)(x-5)}{2} \equiv 4(x-4)(x-5)\space (mod\space 7) \end{align*}

I would be very grateful if someone could give me a detailed explanation.

asked Jan 21 '22 at 02:10

user76333

1

$\bmod 7!:\ ,2\cdot 4 \equiv 1,$ so $, \dfrac{1}2 := 2^{-1}\equiv 4.,$ See the linked dupes on modular fractions and inverses. – Bill Dubuque Jan 21 '22 at 02:54
@BillDubuque Thank you for pointed out. Figured out how to do modular fractions arithmetic. – user76333 Jan 21 '22 at 09:26
Great, glad it helped. – Bill Dubuque Jan 21 '22 at 11:47

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