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Polynomials (x3n)(x2 + 3) Solvable Modulo Any Integer

Andrea M. Hyde, Paul D. Lee and Blair K. Spearman
The American Mathematical Monthly
Vol. 121, No. 4 (April 2014), pp. 355-358
DOI: 10.4169/amer.math.monthly.121.04.355
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Page Count: 4
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Polynomials (x3 − n)(x2 + 3) Solvable Modulo Any Integer
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Abstract We give an infinite family of polynomials that are solvable modulo m for every integer m > 1, yet have no roots in the rational numbers. Such polynomials are called intersective. Our classification uses only techniques available in an undergraduate course in number theory.

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