− 1 × ∑ i = 0 n O I {\displaystyle {\sqrt {\sqrt {\sqrt {-1}}}}\times \sum _{i=0}^{n}{OI}}
設質數p>3,求證：
( p − 1 ) ! 1 + ( p − 1 ) ! 2 + ( p − 1 ) ! 3 + L + ( p − 1 ) ! ( p − 1 ) ≡ 0 ( mod p 2 ) {\displaystyle {\frac {(p-1)!}{1}}+{\frac {(p-1)!}{2}}+{\frac {(p-1)!}{3}}+L+{\frac {(p-1)!}{(p-1)}}\equiv 0{\pmod {p^{2}}}}
