Geodesic
On the sum of two squares and two powers of $k$
Roger Clement Crocker1
1 6 Carlton Mansions 14 Holland Park Gardens London W14 8DW, UK
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 $\geq 2$.
DOI : 10.4064/cm112-2-3
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

Roger Clement Crocker 1

1 6 Carlton Mansions 14 Holland Park Gardens London W14 8DW, UK 
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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. http://geodesic.mathdoc.fr/articles/10.4064/cm112-2-3/

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