2222^5555+5555^2222 chia hết cho 7
[tex]2222^2\equiv 2(mod7)\Rightarrow (2222^2)^3\equiv 2^3=8(mod7)\Rightarrow 2222^6\equiv 1(mod7)\Rightarrow (2222^6)^{925}.2222^5\equiv 4.3\equiv 5(mod7)(1)[/tex]
[tex]5555\equiv 4(mod7)\Rightarrow 5555^3\equiv 64\equiv 1(mod7)\Rightarrow (5555^3)^{740}.5555^2\equiv 2(mod7)(2)[/tex]
[tex](1)+(2)=7\Rightarrow đpcm[/tex]