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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 4. Dividing N by 5, the remainder is 1. What is the smallest possible value of N?

 Oct 23, 2021
 #1
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By the Chinese Remainder Theorem, we have $N \equiv 221 \pmod {315}$

The least such integer is $\boxed{221}$

 Oct 23, 2021
 #3
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This is not 4 digits.

Melody  Oct 24, 2021
 #2
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The smallest possible N == 1,166

 

1,166 mod 9==5

1,166 mod 7==4

1,166 mod 5==1

 Oct 23, 2021

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