# Math Help - find the least positive residue

1. ## find the least positive residue

find the least positive residue of (2^(p+1)) + (p-1)! modulo p if p>3 is prime

2. By Fermat's Little Theorem we have: $2^{p+1}\equiv{4}(\bmod.p)$

And by Wilson's Theorem: $(p-1)!\equiv{-1}(\bmod.p)$

Thus: $2^{p+1}+(p-1)!\equiv{3}(\bmod.p)$