Abstract
Since 1934 Erdős has introduced various methods to derive arithmetic properties of blocks of consecutive integers. This research culminated in 1975 when Erdős and Selfridge (Ill J Math 19:292–301, 1975) established the old conjecture that the product of two or more consecutive positive integers is never a perfect power. It is very likely that the product of the terms of a finite arithmetic progression of length at least four is never a perfect power. In the present paper it is shown how Erdős’ methods have been extended to obtain results for arithmetic progressions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have