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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)

 Nov 16, 2021
 #1
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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.

 Nov 20, 2021

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