scholarly journals A pair of equations in unlike powers of primes and powers of 2

2020 ◽  
Vol 18 (1) ◽  
pp. 662-670
Author(s):  
Yong Cai ◽  
Liqun Hu
Keyword(s):  
Necessary Conditions ◽  
Powers Of 2 ◽  
Prime Squares

Abstract In this article, we show that every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of one prime, one prime squares, two prime cubes, and 187 powers of 2.

ON PAIRS OF ONE PRIME, TWO PRIME SQUARES AND POWERS OF 2

2013 ◽  
Vol 09 (06) ◽  
pp. 1413-1421 ◽  
Author(s):  
ZHIXIN LIU
Keyword(s):  
Necessary Conditions ◽  
Short Paper ◽  
Powers Of 2 ◽  
Prime Squares

In this short paper, it is proved that every pair of large positive odd integers satisfying some necessary conditions can be represented in the form of a pair of one prime, two prime squares and k powers of 2. In particular, we have k = 332.

Two prime squares, four prime cubes and powers of 2

2019 ◽  
Vol 187 (2) ◽  
pp. 143-150
Author(s):  
Xiaodong Zhao
Keyword(s):  
Powers Of 2 ◽  
Prime Squares

A pair of equations in four prime squares and powers of 2

2019 ◽  
Author(s):  
Liqun Hu ◽  
Yafang Kong ◽  
Zhixin Liu
Keyword(s):  
Powers Of 2 ◽  
Prime Squares

On Residue Difference Sets

1953 ◽  
Vol 5 ◽  
pp. 425-432 ◽  
Author(s):  
Emma Lehmer
Keyword(s):  
Necessary Conditions ◽  
Difference Sets ◽  
Difference Set ◽  
Finite Geometries ◽  
Powers Of 2 ◽  
Higher Power ◽  
Modulo P ◽  
The Subject

In recent years the subject of difference sets has attracted a considerable amount of attention in connection with problems in finite geometries [4]. Difference sets arising from higher power residues were first discussed by Chowla [1], who proved that biquadratic residues modulo p form a difference set if (p — l )/4 is an odd square. In this paper we shall prove a similar result for octic residues and develop some necessary conditions which will eliminate all odd power residue difference sets and many others. We also prove that a perfect residue difference set (that is, one in which every difference appears exactly once) contains all the powers of 2 modulo p.

scholarly journals On pairs of equations in unlike powers of primes and powers of 2

2017 ◽  
Vol 15 (1) ◽  
pp. 1487-1494 ◽  
Author(s):  
Liqun Hu ◽  
Li Yang
Keyword(s):  
Necessary Conditions ◽  
Powers Of 2

Abstract In this paper, we obtained that when k = 455, every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of unlike powers of primes and k powers of 2.

ON SUMS OF TWO PRIME SQUARES, FOUR PRIME CUBES AND POWERS OF TWO

2020 ◽  
Vol 102 (2) ◽  
pp. 207-216
Author(s):  
YUHUI LIU
Keyword(s):  
Number Theory ◽  
Goldbach Problem ◽  
Powers Of 2 ◽  
Prime Squares

We prove that every sufficiently large even integer can be represented as the sum of two squares of primes, four cubes of primes and 28 powers of two. This improves the result obtained by Liu and Lü [‘Two results on powers of 2 in Waring–Goldbach problem’, J. Number Theory 131(4) (2011), 716–736].

scholarly journals Four prime squares and powers of 2

2006 ◽  
Vol 125 (4) ◽  
pp. 383-391 ◽  
Author(s):  
Hongze Li
Keyword(s):  
Powers Of 2 ◽  
Prime Squares
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