How many positive integers less than or equal to 6*7*8*9 solve the system of congruences:
m = 5 (mod 6)
m = 4 (mod 7)
m = 3 (mod 8)
+118725 18 I think
HCF(6,7,8) = 2
6*7*8/2 = 168 so it will be mod 168
3*7*8 * 2*9 = 6*7*8*9
3*7*8 * 18 = 6*7*8*9
So i think there will be 18.
It would be good if you come back and comment on my answer.
I've never studied modular arithmetic formally and I am guessing my way a bit.
