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$N$ is a four-digit positive integer. Dividing $N$ by $9$, the remainder is $5$. Dividing $N$ by $7$, the remainder is $3$. Dividing $N$ by $5$, the remainder is $1$. What is the smallest possible value of $N$?

 Sep 12, 2022
 #1
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Using Chinese Remainder Theorem + Modular Multiplicative Inverse, we have:

 

LCM[9, 7, 5]==315

 

N ==315m + 311, where m=0, 1, 2, 3.........etc.

 

When m==3, then:

 

N ==[315 * 3  +  311]==1,256 - the smallest 4-digit intger

 Sep 12, 2022
 #2
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That answer is wrong.

Guest Sep 20, 2022

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