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≡3(mod7),x≡6(mod8),x≡2(mod5). You can either list or use CRT from here. You should get 262.
