Here is another polynomial question. This is from one of the American Math
Competitions for high school students.
I would have to do some research to validate which year and contest it is
from but I think it is from the 1999 Invitational.
Consider the polynomial f(x) = x^2 - 19x + 99. What is the sum of all
positive integers x such that f(x) is the square of an integer?
[This is also an integer between 0 and 999, inclusive.]
I think the contest allows an average of 10 to 12 minutes per problem.
Assume that tools are limited to pencil and paper.
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