Exercise 2.4.12 (Pseudoprime to the base $11$)

Question

Let $m = 3215031751$. Observe that $d = (m-1)/2$ is odd. Show that $11^d \equiv 2129160099 
ot \equiv \pm1 \pmod m$. Deduce that $m$ is composite.

Richard Ganaye · Accepted Answer

\begin{proof} Let $m = 3215031751$. Using the program given in Problem 2, we obtain
$$11^{(m-1)/2} \equiv 2129160099 
ot \equiv \pm1 \pmod m.$$
But
$$11^{m-1} \equiv 1 \pmod m.$$
Therefore $m = 3215031751$ is not spsp($11$). This implies that $m$ is composite ($m$ is is pseudoprime to the base $11$).
\end{proof}

Exercise 2.4.12 (Pseudoprime to the base $11$)

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Exercise 2.4.12 (Pseudoprime to the base $11$)

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