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/