On the sum of two squares and two powers of k

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 -