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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)?

 May 17, 2022
 #1
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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

 May 17, 2022

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