Number Theory

Using Chinese Remainder Theorem, the answer is \(\color{brown}\boxed{1,067}\)

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