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 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 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.

Czech National Awareness in Moravia in the Revolutionary Years 1848/1849

2014 ◽  
Vol 6 (1) ◽  
Author(s):  
František Čapka
Keyword(s):  
Nineteenth Century ◽  
Necessary Conditions ◽  
Cultural Contact ◽  
Significant Change ◽  
Mutual Relations ◽  
High Degree

AbstractThis study focuses on the process of the gradual shaping of Czech national awareness in Moravia from the beginning of the nineteenth century onwards when the necessary conditions for the development of improved mutual relations between the Czech (Slavic) population in the two Lands of the Czech Crown -Bohemia and Moravia - were slowly being formed. Moravia faced a number of handicaps to the development of a national revival in comparison with Bohemia, the most significant of which was the relatively high degree of Germanisation of the land. A change to the image of Moravia came in the revolutionary years 1848/1849, when Czech national awareness spread to broader sections of society in Moravia. The view of Bohemia held by the Moravians underwent significant change and a period of increasingly intensive political and cultural contact between the two lands arose.

SOCIAL PROTECTION IS A GUARANTEE OF FAMILY UNITY

2020 ◽  
Vol 7 (3) ◽  
pp. 89-96
Author(s):  
Dilbar Karshieva ◽  
Keyword(s):  
Social Protection ◽  
Necessary Conditions ◽  
Family Members ◽  
The State ◽  
The Military ◽  
Family Unity

This article demonstrates the great attention and care paid by the state to the military and their families in our country.Social protection of families of military men consists in creating necessary conditions for family members to develop and demonstrate their abilities in socio-economic, cultural, medical and other spheres.

Effective ways to study the works of great ancestors

2020 ◽  
Vol 3 (1) ◽  
pp. 147-149
Author(s):  
Bahodir Kuchkarov
Keyword(s):  
Young People ◽  
Education System ◽  
Necessary Conditions ◽  
Spiritual Values ◽  
Educational Changes ◽  
Younger Generation

In Uzbekistan, special attention is paid to the study of historical, national and spiritual values ​​in the context of socio-economic, spiritual and educational changes. All necessary conditions for the education of young people are now created. The fundamental task of today is to radically change the education system, to educate the younger generation in the spirit of enlightenment, and to encourage patriotism and creativity of the young. In this article, I will discuss the importance of studying the works of ancient great thinkers and to conduct lessons by using topics related to the personality and works of great ancestors in terms of shaping the students' spiritual outlook.

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