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/