Commun. Korean Math. Soc. 2003 Vol. 18, No. 4, 661-667 Printed December 1, 2003
Seon-Hong Kim Chosun University
Abstract : In this paper, we show, for a positive integer $m$ and a large odd integer $n$, the polynomial equation $$ \prod_{k=0}^n (x-k^{1+\frac 1m})+\prod_{k=n+1}^{2n+1} (x- k^{1+\frac 1m})=0 $$ has a real zero on $$ \left( (n+1)^{1+\frac 1m}, \, \, (n+1)^{1+\frac 1m}+\frac 12\right) $$ and $$\left( (n+1)^{1+\frac 1m}+\frac 12, \, \,(n+2)^{1+\frac 1m}\right), $$ respectively.
