Every sufficiently large natural number can be written as $p+n_1^2+n_2^2$ for some $n_1,n_2$ - natural numbers and $p$ - prime number.
I saw this used in russian article, but it was given as a fact without comment. Does this theorem have a name?
What methods are used in proofs of theorems stating that sufficiently large integers can be written in some forms? The only somehow similar thing I know is the Lagrange's four-square theorem. But if we involve primes in the representation, similar methods can't work I guess