find the least positive residue of (2^(p+1)) + (p-1)! modulo p if p>3 is prime
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By Fermat's Little Theorem we have: $\displaystyle 2^{p+1}\equiv{4}(\bmod.p)$ And by Wilson's Theorem: $\displaystyle (p-1)!\equiv{-1}(\bmod.p)$ Thus: $\displaystyle 2^{p+1}+(p-1)!\equiv{3}(\bmod.p)$
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