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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 = 2 (mod 9)

m = 1 (mod 10)

 
 Jul 19, 2021
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Using CRT + MMI

m = 5 (mod 6)

m = 4 (mod 7)

m = 3 (mod 8)

m = 2 (mod 9)

m = 1 (mod 10)

 

Product(6, 7, 8, 9)==3,024

 

m ==2,520k  +  11, where k==0,1,2,3........etc.

 

m==2,520 is smallest integer that satisfies all 5 congruences. The next number would be: 2,520 x 2 ==5,040.

 
 Jul 19, 2021

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