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?
Constructing pseudoprimes to the base 3.
2
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number-theory
prime-numbers
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0Did you mean $2^{n-1}$, or $2^n - 1$? I wasn't sure. – 2012-04-29
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0Sorry, (2^n)-1. – 2012-04-29
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1I presume you mean Fermat pseudoprimes? – 2012-04-29
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0Okay... 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