In his 1825 paper, Lejeune Dirichlet proved that the equation $x^5 + y^5 = cz^5$ has no nontrivial solution with x and y coprime integers and z integer for a rather large class of integers c. His paper can be read on the site Gallica :
http://gallica.bnf.fr/ark:/12148/bpt6k5842885h/f2.item.zoom
but the visualization is very bad.