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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)

 Nov 16, 2021
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 6*7*8*9 ==3024

 

m = 5 (mod 6)

m = 4 (mod 7)

m = 3 (mod 8)

m = 2 (mod 9)

m = 1 (mod 10)

 

LCM(6, 7, 8, 9, 10)==2520

 

m ==2520n + 11, where n==0, 1, 2, 3.........etc.

When n=1,  m==2520 + 11 ==2531 - the smallest m under 3024 that satisfies all 5 congruences.

 Nov 16, 2021

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