Question

From the equation $(a+b)^p=a^p+b^p$ in $G F_{p^n}$, derive the equation $(a-b)^p=$ $a^p-b^p$.

    From the equation $(a+b)^p=a^p+b^p$ in $G F_{p^n}$, derive the equation $(a-b)^p=$ $a^p-b^p$.

Applied Algebra: Codes, Ciphers and Discrete Algorithms

Applied Algebra: Codes, Ciphers and Discrete Algorithms

Darel W. Hardy, Fred… 2nd Edition

Chapter 10, Problem 13

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Step 1

This equation holds due to the properties of the Frobenius automorphism in a finite field of characteristic $p$, where $(x+y)^p = x^p + y^p$ for any $x, y \in GF(p^n)$. Show more…

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From the equation $(a+b)^p=a^p+b^p$ in $G F_{p^n}$, derive the equation $(a-b)^p=$ $a^p-b^p$.

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