Pseudoprimes

Definition. A composite $n$ with $a^{n-1}\equiv1\pmod n$ for some $a$ coprime to $n$.

Compute. $341=11\cdot31$.
- mod $11$: $2^{10}\equiv1$, $340=34\cdot10$, so $2^{340}\equiv1$.
- mod $31$: $2^5=32\equiv1$, $340=68\cdot5$, so $2^{340}\equiv1$.

CRT. $2^{340}\equiv1\pmod{341}$.

Conclusion. $341$ is a Fermat pseudoprime to base $2$.