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When $n$ is a pseudo prime to the base 2, $2^{n}-1$ is also a pseudo prime to the base 2. This implies there are infinitely many pseudoprimes to the base 2. Then, how can I construct pseudoprimes to the base 3 from known pseudoprime to the base 3 in similar way to show that there are infinitely many pseudo primes to the base 3?

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    Did you mean $2^{n-1}$, or $2^n - 1$? I wasn't sure.2012-04-29
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    Sorry, (2^n)-1.2012-04-29
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    I presume you mean Fermat pseudoprimes?2012-04-29
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    Okay... your question boils down to "given a base-$3$ Fermat pseudoprime, construct another base-$3$ Fermat pseudoprime from it". Am I right?2012-04-29

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