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On a Theorem of Prachar Involving Prime Powers
-
Taiyu Li
and
Hengcai Tang
Published/Copyright:
May 31, 2012
Abstract.
Let p, with or without subscripts, always denote a prime number.
In this paper we are able to establish two localized results on a theorem of Prachar which states that
almost all positive even integers n can be written as 
. As a consequence of one result, we prove additionally that each sufficiently large odd integer N can be represented as 
with 
for 
.
Received: 2011-01-09
Accepted: 2011-10-05
Published Online: 2012-05-31
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Unlike Powers of Primes;
Circle Method;
Exponential Sums;
Distribution of Primes
Articles in the same Issue
- Masthead
- On a Theorem of Prachar Involving Prime Powers
- A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants
- A Recurrence Related to the Bell Numbers
- Sum-Product Estimates Applied to Waring's Problem over Finite Fields
- Communal Partitions of Integers
- On Computation of Exact van der Waerden Numbers
- On the Complexity of Chooser–Picker Positional Games
- Partition of an Integer into Distinct Bounded Parts, Identities and Bounds
- A Correlation Identity for Stern's Sequence
- Primitive Prime Divisors in Zero Orbits of Polynomials
