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)
m = 5 (mod 9)?
+118608
break the mods into their prime factors
6=2*3
7
8=2*2*2
9=3*3
So 6,7,8 and 9 will all go into 2*3*7*2*2*3= 6*7*4*3 = 504
There will be 1 solution less than 504 and then 1 solution for each following product of 504
6*7*8*9 = [6*7*4*3]* 6
So there will be 6 solutions less than 6*7*8*9
