How can I show that $n = 1373653$ is a strong pseudoprime to base $3$? I found this question as an exercise in a book I'm currently reading (which unfortunately doesnt provide a solution to this problem). My attempt: Using Miller's test to the base $3$, I have to show that $3^{343413} = 3^{7*23*27*79} \equiv 1$ (mod $829$) and (mod $1657$). I want to solve this question using my calculator as little as possible. Thanks in advance!
2026-03-26 11:04:14.1774523054
Show that $1373653$ is a strong pseudoprime to base $3$
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