By developing the method of Wooley on the quadratic Waring-Goldbach problem, we prove that all sufficiently large even integers can be expressed as a sum of four squares of primes and 46 powers of 2.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-3-4, author = {Lilu Zhao}, title = {Four squares of primes and powers of 2}, journal = {Acta Arithmetica}, volume = {166}, year = {2014}, pages = {255-271}, zbl = {1307.11104}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-3-4} }
Lilu Zhao. Four squares of primes and powers of 2. Acta Arithmetica, Tome 166 (2014) pp. 255-271. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-3-4/