Four theorems of the author on the subject are given without proofs.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-19, author = {A. Schinzel}, title = {On the congruence f(x) + g(y) + c [?] 0 (mod xy)}, journal = {Banach Center Publications}, volume = {108}, year = {2016}, pages = {255-257}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-19} }
A. Schinzel. On the congruence f(x) + g(y) + c ≡ 0 (mod xy). Banach Center Publications, Tome 108 (2016) pp. 255-257. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-19/