Abstract. We give a short proof of a recent result of Hare, McKinnon and Sinclair on divisibility of the resultant of two polynomials whose roots are prime powers of a given monic polynomial. Our proof is based on Smyth's congruence involving powers of conjugate algebraic integers. An application to the Mahler measure of a polynomial is also given.

AMS Subject Classification (1991): 11C08, 11R04, 11R09

Keyword(s): polynomial, resultant, Mahler's measure

Received December 18, 2009. (Registered under 6439/2009.)