Question

求同余方程的解 x≡1(mod5)x≡5(mod6)x≡4(mod7)x≡10(mod11)是求满足上述同余方程的解

Answer 1

x≡1(mod5),

x≡5(mod6),

x≡4(mod7),

x≡10(mod11) ,

lcm(5,6,7,11)=2310,

lcm(6,7,11)=462,

lcm(5,7,11)=385,

lcm(5,6,11)=330,

lcm(5,6,7)=210,

x=1386+1925+1320+2100-2310i

=6731-2310i,i∈Z

x=2111+2310k,k∈N