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.)

The idea is correct, but 98=(-7)(-1)(1)(2)(7). I found this method on my own, and asked for squares since that meshed well with f(b)=9... I could have also asked for f(b)=3^n, or f(b)=10^n-1, but squares seemed nicer! :-)