Question

Using Chinese Remainder Theorem solve for X:

x = 2 (mod 3)

x = 4 (mod 5)

x = 5 (mod 8)

I have the answer the professor gave me, but I can`t understand what`s going on. So if you could please go over the answer and explain, it would help a lot.

x = 2 (mod 3)

x = 3a + 2

3a + 2 = 4 (mod 5)

(2) 3a = 2 (2) (mod 5) -----> why number 2?

a= 4 (mod 5) ---------> What happened with 6?

a = 5b + 4

x = 3 (5b + 4) + 2 --------> what`s going on here?

x = 15 b + 14

15b + 14 = 5 (mod 8)

7b + 6 = 5 (mod 8)

7b = -1 (mod 8)

(7) 7b = 7 (mod 8) (7)

b = 1 (mod 8)

b = 8c + 1

x = 15 (8c + 1) + 14

x + 120c + 29

x = 29 (mod 120)

Answer 1