Question

Show that in $Z_{p+1}$, where $p$ is prime, only one element passes the primality test $x^{m-1}=1$. (In this case, $m=p+1$.)

   Show that in $Z_{p+1}$, where $p$ is prime, only one element passes the primality test $x^{m-1}=1$. (In this case, $m=p+1$.)

Discrete Math in Computer Science

Discrete Math in Computer Science

Bogart, Stein.

Chapter 2, Problem 11

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Step 1

We are working in the ring of integers modulo \( p+1 \), denoted as \( \mathbb{Z}_{p+1} \), where \( p \) is a prime number. The elements of \( \mathbb{Z}_{p+1} \) are \( \{0, 1, 2, \ldots, p\} \). Show more…

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Show that in $Z_{p+1}$, where $p$ is prime, only one element passes the primality test $x^{m-1}=1$. (In this case, $m=p+1$.)

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