top
It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 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 ≥ 2.
Roger Clement Crocker. "On the sum of two squares and two powers of k." Colloquium Mathematicae 112.2 (2008): 235-267. <http://eudml.org/doc/283409>.
@article{RogerClementCrocker2008, abstract = {It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 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 ≥ 2.}, author = {Roger Clement Crocker}, journal = {Colloquium Mathematicae}, keywords = {sums of two squares; sums of powers}, language = {eng}, number = {2}, pages = {235-267}, title = {On the sum of two squares and two powers of k}, url = {http://eudml.org/doc/283409}, volume = {112}, year = {2008}, }
TY - JOUR AU - Roger Clement Crocker TI - On the sum of two squares and two powers of k JO - Colloquium Mathematicae PY - 2008 VL - 112 IS - 2 SP - 235 EP - 267 AB - It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 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 ≥ 2. LA - eng KW - sums of two squares; sums of powers UR - http://eudml.org/doc/283409 ER -