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Let n>m be positive integers. Polynomials of the form zn±zm±1 are called Borwein trinomials. Using an old result of Bohl, we derive explicit formulas for the number of roots of a Borwein trinomial inside the unit circle |z|<1. Based on this, we determine all Borwein trinomials that have a complex Pisot number as a root. There are exactly 29 such trinomials.
Drungilas et al. (Tue,) studied this question.