On the Integrality of the Elementary Symmetric Functions of 1, 1/3, . . . , 1/(2n − 1)

Abstract

Abstract Erdős and Niven proved that for any positive integers m and d, there are only finitely many positive integers n for which one or more of the elementary symmetric functions of 1/m, 1/(m + d), . . . , 1/(m + nd) are integers. In this paper, we show that if n ≥ 2, then none of the elementary symmetric functions of 1, 1/3, . . . , 1/(2n − 1) is an integer