回复：N = 1942

多谢了。老师没给答案。把16 换成 8。

2014 = 2 X 19 X 53, 1004 = 2 X 2 X 251

-->
1004 | (2009N + 2019X2014)
8       | (2009N + 2019X2014) (这里是否还需要考虑 19 & 53?)

--> N + 66 =0 (mod 1004)
     N + 2   =0 (mod 8)

--> 1004P - 66 = 9Q - 2
--> 251 P = 2Q + 16
--> P = 0 (mod 2).
--> Take P = 2 --> N = 1004 P - 66 = 2008 - 66 = 1942.

验证一下：N = 1942

2009X1942+2014X2019 = 7967744 = 2^10 X 31 X 251
2014X1942 = 2^2 X 19 X 53 X 971

So A/B
= (2^8 X 31 X 251) / (19 X 53 X 971) (lowest common fraction)
= (1004 X 2^6 X 31)/(19X53X971)