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.
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