Some Number Theoretic Applications of the Smallest Denominator Function

نویسنده

  • Z. BOROS
چکیده

We show that the smallest denominator function can be treated with a minimum amount of number theory. Moreover, this function can be used to nicely prove a number of fundamental divisibility and irrationality results. Acta Mathematica Academiae Paedagogicae Ny regyh aziensis 15 (1999), 19{26 www.bgytf.hu/~amapn

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Smallest Denominator Function and the Riemann Function

In this paper, we initiate a rigorous and detailed study of the smallest denominator function and the Riemann function. For this, we rst establish some basic facts about real numbers and the divisibility of integers.

متن کامل

SOME SIMILARITY MEASURES FOR PICTURE FUZZY SETS AND THEIR APPLICATIONS

In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similar...

متن کامل

THE ORDER GRAPHS OF GROUPS

Let $G$ be a group. The order graph of $G$ is the (undirected)graph $Gamma(G)$,those whose vertices are non-trivial subgroups of $G$ and two distinctvertices $H$ and $K$ are adjacent if and only if either$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate theinterplay between the group-theoretic properties of $G$ and thegraph-theoretic properties of $Gamma(G)$. For a finite group$G$, we s...

متن کامل

Some results on the complement of a new graph associated to a commutative ring

The rings considered in this article are commutative with identity which are not fields. Let R be a ring. A. Alilou, J. Amjadi and Sheikholeslami introduced and investigated a graph whose vertex set is the set of all nontrivial ideals of R and distinct vertices I, J are joined by an edge in this graph if and only if either ann(I)J = (0) or ann(J)I = (0). They called this graph as a new graph as...

متن کامل

الگوریتم ژنتیک با جهش آشوبی هوشمند و ترکیب چند‌نقطه‌ای مکاشفه‌ای برای حل مسئله رنگ‌آمیزی گراف

Graph coloring is a way of coloring the vertices of a graph such that no two adjacent vertices have the same color. Graph coloring problem (GCP) is about finding the smallest number of colors needed to color a given graph. The smallest number of colors needed to color a graph G, is called its chromatic number. GCP is a well-known NP-hard problems and, therefore, heuristic algorithms are usually...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999