TITLE: All natural solutions of $2x^2-1=y^{15}$
QUESTION [5 upvotes]: How can I find all positive integers $x$ and $y$ such that $2x^2-1=y^{15}$?
PS. See here.

REPLY [4 votes]: There are no solutions other then $(x,y)=(1,1)$
See http://rmmc.asu.edu/abstracts/rmj/vol31-2/lucapag1.pdf