Problem of the Week 1016

Peculiar Polynomials

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Call a monic polynomial peculiar if its coefficients are in arithmetic progression and its roots are integers. One example is x^2-1, whose coefficients are 1, 0, -1 with roots -1 and 1. Find all peculiar polynomials of degree at least 2.

Source: Bill Sands, Univ. of Calgary, Crux Mathematicorum, May 2003, p. 208.

© Copyright 2004 Stan Wagon. Reproduced with permission.