f(x)=anxn+⋯+a1x+a0≡0(mod p),an≢0(mod p)f\left(x\right)=a_nx^n+\cdots+a_1x+a_0\equiv0\left(\mod p\right) ,a_n\not\equiv0\left(\mod p\right)f(x)=anxn+⋯+a1x+a0≡0(modp),an≡0(modp)
f(x)=q(x)(xp−x)+r(x)f\left(x\right)=q\left(x\right)\left(x^p-x\right)+r\left(x\right)f(x)=q(x)(xp−x)+r(x) f(x)≡0(mod p)⟺r(x)≡0(mod p)f\left(x\right)\equiv0\left(\mod p\right)\Longleftrightarrow r\left(x\right)\equiv0\left(\mod p\right)f(x)≡0(modp)⟺r(x)≡0(modp)
最后更新于3年前