Abstract
In 1919 George Polya [6] published Als Kuriosum the following result. Let n > 17. If among the values assumed by an integral-coefficient polynomial of degree n, the same prime integer p, with plus or minus sign, appears n times, then the polynomial is either irreducible or the product of two irreducible factors of equal degree. The conclusion of this theorem is intriguing, but the portion of the hypothesis that limits its applicability to polynomials of at least the 17th degree indicates why it was published as a curiosity. Fortunately new methods [3] have shown that this theorem is true for all odd n > 3 and even n > 6. These extensions were discussed and the following examples given in [1] to show that the theorem does not hold for n =3 and n =6:
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