同余式的基本性质

1. \(a\equiv a(\bmod m)\)
2. \(a\equiv b(\bmod m)\to b\equiv a(\bmod m)\)
3. \(a\equiv b(\bmod m) \wedge b\equiv c(\bmod m)\to a\equiv c(\bmod m)\)
4. \(ac\equiv bc(\bmod p ) \to a \equiv b(\bmod \frac{p}{gcd(c,p)})\)
5. \(a\equiv b(\bmod cd) \to a\equiv b(\bmod d)\)
6. \(a\equiv b(\bmod d)\wedge a\equiv b(\bmod c) \to a\equiv b(\bmod lcm(c,d))\)
7. \(a\equiv b(\bmod p)\to \forall c\in\mathbb{Z}\mid (a+c)\equiv (b+c)(\bmod p)\)
8. \(a\equiv b(\bmod p)\to \forall c\in\mathbb{Z}\mid (a\times c)\equiv (b\times c)(\bmod p)\)
9. \(a\equiv b(\bmod p)\to \forall c\in\mathbb{Z}\mid (a^c)\equiv (b^c)(\bmod p)\)