Problem
NT-B2-M04-P016 No Such Primes
#16
★★★★☆ Level 4 of 5
Find all primes \(p\) such that \(p\mid2^{p-1}+1\).
Handle \(p=2\), then apply Fermat.
For \(p=2\), \(2^{p-1}+1=3\) is not divisible by \(2\). If \(p\) is odd, Fermat gives \(2^{p-1}\equiv1\pmod p\). Then \(2^{p-1}+1\equiv2\pmod p\), not \(0\). Answer: there are no such primes.
Short but useful problem on the special case \(p=2\).