Perfect power Riesel numbers

A Riesel number k   is an odd positive integer such that k⋅2n−1k⋅2n−1 is composite for all integers n≥1n≥1. In 2003, Chen proved that there are infinitely many Riesel numbers of the form krkr, when r≢0,4,6,8(mod12), and he conjectured that such Riesel powers exist for all positive integers r  . In 2008, Filaseta, Finch and Kozek extended Chen's theorem slightly by constructing Riesel numbers of the form k4k4 and k6k6. In 2009, Wu and Sun provided more evidence to support Chen's conjecture by showing that there exist infinitely many Riesel numbers of the form krkr for any positive integer r   that is coprime to 15015. In this article, we extend the results of Wu and Sun by proving that there exist infinitely many Riesel numbers of the form krkr for any positive integer r that is coprime to 105.