On the sum of two squares and two powers of k

• Autorzy: Roger Clement Crocker
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11A41: Primes
• 11P32: Goldbach-type theorems; other additive questions involving primes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 112
• Numer: 2
• Strony: 235-267

Daty

wydano

2008

Twórcy

autor

Roger Clement Crocker

• 6 Carlton Mansions, 14 Holland Park Gardens, London W14 8DW, UK

Identyfikatory

DOI

10.4064/cm112-2-3