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Problem of the Week 857

An Elusive Quadratic

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February 28, 1998 sees the sixth annual Konhauser Problemfest, a problem competition for several colleges in Minnesota dedicated to the memory of problemist and Macalester professor Joe Konhauser. Joe started the problem of the week here in 1968. Here is a problem that was used on the first KP in 1993. Joe, who died a few years ago, was always fond of polynomial problems, and this one came from his files.

Find a second-degree polynomial with integer coefficients, p(x) = ax2 + bx + c, such that p(1), p(2), p(3), and p(4) are perfect squares (that is, squares of integers), but p(5) is not.

© Copyright 1998 Stan Wagon. Reproduced with permission.

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The Math Forum

2 October 1998