Find all numbers r for which the system of congruences

x = r (mod 6),

x = 9 (mod 20),

x = 4 (mod 45)

has a solution.

*Sorry I didn't know how to put the sign with 3 straight horizontal lines so I just made them equal signs.

Guest Aug 3, 2017

edited by
Guest
Aug 3, 2017

#1**+1 **

x mod 20=9, x mod 45=4, x mod 6 =r, solve for x, r

By simple iteration, the smallest positive integer that satisfies all the congruences is**=49**

**Check:**

**49 / 20 = 2 with a remainder of 9, and:**

**49 /45 =1 with a remainder of 4, and:**

**49 / 6 =8 with a remainder of 1. Therefore:**

**r=1 and x=49**

Guest Aug 3, 2017