Cryptology HW Question:

Problem 7. A group of people are arranging themselves for a parade. If they line up five to a row, 1 person is left over. If they line up six to a row, 2 people are left over, and if they line up seven to a row, four people are left over. What is the smallest possible number of people in the group. Explain. What is the next smallest element? Explain (Hint: apply the CRT.)