# How do I prove that that 91 is/is not a pseudoprime to base 2

I know that Fermat Pseudoprime formula is $a^{p-1} \equiv 1 \mod{p}$ c but in this case $p$ is not prime.

How do I prove that that $91$ is/is not a pseudoprime to base $2$.

$91$ is not prime , but $91=7*13$. Moreover, $$2^{90}= 2^{6*15}=64^{15} \equiv (-1)^{15} \equiv -1 \mod{13}$$ since $13 *5 =65$. Hence $13 \nmid 2^{91-1 }-1$ as $13 \nmid 2^{91-1 }+1$ and so $91 \nmid 2^{91-1 }$. Therefore $91$ is not Fermat Pseudoprime of base 2.