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Polynomials (x3 − n)(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
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.04.355
Page Count: 4
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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.
Copyright the Mathematical Association of America 2014