It is proved that all sufficiently large integers satisfying the necessary congruence conditions mod 24 are sums of four squares prime in pairs.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-2-3, author = {A. Schinzel}, title = {On Sums of Four Coprime Squares}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {61}, year = {2013}, pages = {109-111}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-2-3} }
A. Schinzel. On Sums of Four Coprime Squares. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) pp. 109-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-2-3/