An arithmetic property of Mahler's series

1997 ◽  
Vol 13 (3) ◽  
pp. 407-412 ◽  
Author(s):  
Zhu Yaochen
Keyword(s):  
Arithmetic Property ◽  
Mahler's Series

scholarly journals Solving Problems with Smooth Sequences that are Subject to Local Restrictions

2019 ◽  
Vol 9 (1) ◽  
pp. 3987-3994
Keyword(s):  
Literature Review ◽  
Learning Process ◽  
Practical Significance ◽  
Arithmetic Property ◽  
Detailed Review

This article discusses the options that arise when solving problems with smooth sequences that are subject to local restrictions. It also continues the cycle of work on the study of smooth sequences and supplements the literature in the field of the study of this arithmetic property. The relevance of the current research is that the smooth sequences simulate the motion of the bodies taking into account the resistance of the medium. The methodology is in solving problems and proving theorems by calculating the formulas and building the graphs and providing the comments on them. It should be noted that when conducting a literature review about such problems and their solution, we noticed a lack of a detailed review and compactness of information. Thus, this work has a scientific novelty and, as a result, practical significance for the learning process. The paper presents a detailed description of the solutions of smooth sequences on the 1st, 2nd, 3rd differences; it also provides evidence with explanations of the theorems, gives illustrations of graphs of sequences under different conditions. The results of the study may be applicated to spaceship building and ballistics. Besides this, the article is supplemented with data in tables shown in the Appendices.

scholarly journals Arithmetic, enumerative induction and size bias

Synthese ◽  
2021 ◽  
Author(s):  
A. C. Paseau
Keyword(s):  
Number Theory ◽  
Natural Number ◽  
Arithmetic Property ◽  
Number Sequence ◽  
Size Bias ◽  
Goldbach’S Conjecture ◽  
Best Argument ◽  
Goldbach's Conjecture

AbstractNumber theory abounds with conjectures asserting that every natural number has some arithmetic property. An example is Goldbach’s Conjecture, which states that every even number greater than 2 is the sum of two primes. Enumerative inductive evidence for such conjectures usually consists of small cases. In the absence of supporting reasons, mathematicians mistrust such evidence for arithmetical generalisations, more so than most other forms of non-deductive evidence. Some philosophers have also expressed scepticism about the value of enumerative inductive evidence in arithmetic. But why? Perhaps the best argument is that known instances of an arithmetical conjecture are almost always small: they appear at the start of the natural number sequence. Evidence of this kind consequently suffers from size bias. My essay shows that this sort of scepticism comes in many different flavours, raises some challenges for them all, and explores their respective responses.

An arithmetic property of profinite groups

1982 ◽  
Vol 37 (1) ◽  
pp. 11-17 ◽  
Author(s):  
Wolfgang Herfort
Keyword(s):  
Arithmetic Property ◽  
Profinite Groups
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