請問競賽ㄧ題

[victy614]

題目是
設p為滿足下列條件的質數:
有一整係數多項式函數f(x)使得f(12) = 2010, f(p) = 1879,
試求所有這種質數p的和 = ?

煩請各位老師解答,感謝!

[thepiano]

令 f(x) = (x - 12)q(x) + 2010
f(p) = (p - 12)q(p) + 2010 = 1879
(p - 12)q(p) = -131
p - 12 = 1 or -131 or -1 or 131
p = 13 or 11