On the sum of two squares and two powers of $k$
Tom 112 / 2008
Colloquium Mathematicum 112 (2008), 235-267
MSC: Primary 11P32; Secondary 11A41.
DOI: 10.4064/cm112-2-3
Streszczenie
It can be shown that the positive integers representable as the sum of two squares and one power of $k$ ($k$ any fixed integer $\geq 2$) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of $k$ also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of $k$, $k$ again any fixed integer $\geq 2$.
