A polynomial f in the set {Xⁿ+Yⁿ, Xⁿ +Yⁿ-Zⁿ, Xⁿ +Yⁿ+Zⁿ, Xⁿ +Yⁿ-1} lends itself to an elementary proof of the following theorem: if the coordinate ring over ℚ of f is factorial, then n is one or two. We give a list of problems suggested by this result.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-2-9, author = {Peter Malcolmson and Frank Okoh and Vasuvedan Srinivas}, title = {Factorial Fermat curves over the rational numbers}, journal = {Colloquium Mathematicae}, volume = {144}, year = {2016}, pages = {285-300}, zbl = {1337.13018}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-2-9} }
Peter Malcolmson; Frank Okoh; Vasuvedan Srinivas. Factorial Fermat curves over the rational numbers. Colloquium Mathematicae, Tome 144 (2016) pp. 285-300. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-2-9/