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.