On the sum of two squares and two powers of $k$
Colloquium Mathematicum, Tome 112 (2008) no. 2, pp. 235-267
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $\geq 2$.
Keywords:
shown positive integers representable sum squares power fixed integer geq have positive density which follows those integers representable sum squares powers have positive density purpose paper there infinity positive integers representable sum squares fewer powers again fixed integer geq
Affiliations des auteurs :
Roger Clement Crocker 1
@article{10_4064_cm112_2_3,
author = {Roger Clement Crocker},
title = {On the sum of two squares and two powers of $k$},
journal = {Colloquium Mathematicum},
pages = {235--267},
publisher = {mathdoc},
volume = {112},
number = {2},
year = {2008},
doi = {10.4064/cm112-2-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm112-2-3/}
}
Roger Clement Crocker. On the sum of two squares and two powers of $k$. Colloquium Mathematicum, Tome 112 (2008) no. 2, pp. 235-267. doi: 10.4064/cm112-2-3
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