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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 2. What is the smallest possible value of  N?

 Mar 8, 2022
 #2
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Using Chinese Remainder Theorem, the answer is \(\color{brown}\boxed{1,067}\)

 Mar 8, 2022
 #3
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1008 mod 9 = 0    

   need = 5                    so start with 1013              (1008 +5)

 

then continue adding 9's

  1022        looking for easily seen remainder two when divided by 5  

                   but 1022 does not have remainder 3 when divided by 7 so continue ading 9's

1031

1040

1049

1058

1067       <=====     mod 9 =5     mod 7 = 3      mod 5 = 2

 Mar 8, 2022

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