Problem 23E

Solve the system of congruences in Exercise 20 using the method of back substitution.

Reference Exercise 20

Use the construction in the proof of the Chinese remainder theorem to find all solutions to the system of congruences

x=2(mod 3), x=1 (mod 4), and x=3 (mod 5)

Solution:

Step 1:

In this problem, we need to solve the system of congruence.