Let f(x) be a nonconstant polynomial in x with integer coefficients and suppose that for five distinct integers a1, a2, a3, a4, a5, one has f(a1)= f(a2)= f(a3)= f(a4)= f(a5)= 2.

Find all integers b such that f(b)= 9.

(In reply to Solution (spoiler) by e.g.)

Thus the reason that f(n) cannot be 9 when n is an integer is that 7 is a prime, and not that 9 is a square.

Posted by Richard on 2006-05-26 15:03:58