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Salem number
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{{Use American English|date = March 2019}} {{Short description|Type of algebraic integer}} [[File:Salem numbers.svg|thumb|300px|Plot of the roots of Lehmer's [[polynomial]], with the corresponding Salem number near <math>x=1.17628</math> in gold.]] In [[mathematics]], a '''Salem number''' is a [[real number|real]] [[algebraic integer]] <math>\alpha > 1</math> whose [[conjugate roots]] all have [[absolute value]] no greater than 1, and at least one of which has absolute value exactly 1. Salem numbers are of interest in [[Diophantine approximation]] and [[harmonic analysis]]. They are named after [[Raphaël Salem]].
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