x ≡ 0 mod 2

x ≡ 1 mod 3

x ≡ 2 mod 5

x ≡ 3 mod 7

a. What is the smallest x?

b. What is the largest 4-digit x?

x = 52 + 210k, where k is any integer

10000/210 ~= 47.6

so the answer to part b is either 52+47*210 or 52+46*210.

52+47*210 = **9922**

Since it is under 10,000, this is the answer