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) =ax^{2}+bx+c, such thatp(1),p(2),p(3), andp(4) are perfect squares (that is, squares of integers), butp(5) is not.

© Copyright 1998 Stan Wagon. Reproduced with permission.

2 October 1998