389,635 research outputs found
The elementary symmetric functions of a reciprocal polynomial sequence
Erd\"{o}s and Niven proved in 1946 that for any positive integers and
, there are at most finitely many integers for which at least one of the
elementary symmetric functions of are
integers. Recently, Wang and Hong refined this result by showing that if , then none of the elementary symmetric functions of is an integer for any positive integers and . Let be a
polynomial of degree at least and of nonnegative integer coefficients. In
this paper, we show that none of the elementary symmetric functions of is an integer except for with being
an integer and .Comment: 4 pages. To appear in Comptes Rendus Mathematiqu
- …