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What is the least positive integer which when divided by 5 gives a remainder of 4, when divided by 6 gives a remainder of 5, when divided by 7 gives a remainder of 0, when divided by 8 gives a remainder of 1, when divided by 9 gives a remainder of 2, and when divided by 10 gives a remainder of 9?

 Feb 11, 2022
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N mod 5==4

N mod 6 ==5

N mod 7==0

N mod 8==1

N mod 9==2

N mod 10==9

 

Using "adjusted" CRT + MMI, we have:

 

2,520n +  2009,  where n==0, 1, 2, 3.......etc.

when n==0, the smallest N that satisfies all 6 congruences is:

 

N==2009

 Feb 11, 2022

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