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.
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
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