Vol. 36, No. 1, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
On the sum of a prime and of two powers of two

Roger Clement Crocker

Vol. 36 (1971), No. 1, 103–107
Abstract

lt has been shown by different methods that there is an infinity of positive odd integers not representable as the sum of a prime and a (positive) power of 2, thus disproving a conjecture to the contrary which had been made in the nineteenth century. The question then arises as to whether or not all sufficiently large positive odd integers can be represented as the sum of a prime and of two positive powers of 2; that is, as p + 2α + 2b, where a,b > 0 and p is prime. (The corresponding question has been discussed for bases other than 2 but is really quite trivial.) Theorem I gives a negative answer to this question.

Theorem I. There is an infinity of distinct, positive odd integers not representable as the sum of a prime and of two positive powers of 2.

Mathematical Subject Classification
Primary: 10.05
Milestones
Received: 3 September 1969
Published: 1 January 1971
Authors
Roger Clement Crocker