# Journal of the Ramanujan Mathematical Society

Volume 35, Issue 1, March 2020  pp. 23–33.

Sums of fifth powers being a perfect power: A special case

Authors:  Pranabesh Das, Pallab Kanti Dey and Sudhansu Sekhar Rout
Author institution:Pure Mathematics, University of Waterloo, 200 University Avenue West Waterloo, Ontario, Canada

Summary:  In this article, we are interested in perfect powers concerning weighted sums of consecutive fifth powers. More precisely, we prove that sums of three consecutive odd (or, even) fifth powers never be a perfect power. We also prove that there is no perfect power in alternating sums of five consecutive fifth powers.