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# 素数模的同余式简化

$$f\left(x\right)=a\_nx^n+\cdots+a\_1x+a\_0\equiv0\left(\mod p\right) ,a\_n\not\equiv0\left(\mod p\right)$$

> $$f\left(x\right)=q\left(x\right)\left(x^p-x\right)+r\left(x\right)$$ $$f\left(x\right)\equiv0\left(\mod p\right)\Longleftrightarrow r\left(x\right)\equiv0\left(\mod p\right)$$