A box contains many candies. If 3 candies are taken away, the rest can be shared evenly among 7 people. If 6 are taken away, the rest can be shared evenly among 8 people. If 3 candies are added, then the box can be shared evenly among 5 people. What is the smallest number of candies in the box?
+605 \(x\equiv 3\pmod{7}, x\equiv 6\pmod{8}, x\equiv 2\pmod{5}\). You can either list or use CRT from here. You should get 262.
