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发布网友发布时间：2023-10-15 20:53

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热心网友时间：2024-12-03 22:35

It is known to all that number theory function mean value occupies very important location in estimating that problem studies in number theory ,a lot of famous number theory difficult problem goes hand in hand all with that. Get any substantiality as a result in this one field progress to surely will play arrive at important push role to development of number theory! A few Smarandache functions mean value problem and a few functions character the main body of a book has been studied. And about the function mean value,the problem Smarandache function mean value the main body of a book has been studied is estimated, has got the style advancing graally about one is fairly good; And that and the function mean value having studied the figure that the Samarandache professor has brought forward, the concrete formula that mean value calculates with the function of having got a figure; And the mean value having studied Fibonacci progression and the Lucas progression counting function, has given formula out about calculative few of counting function mean value are concrete; And have defined broad wide Lucas progression, some character of the progression having discussed broad wide Lucas. Concretely, as a matter of fact, main the main body of a book achievement includes several aspect of the following: 1. Problem studies Smarandache function mean value occupying very important location in number theory , it has close something to do with a lot of number theory function mean value. The elementary and analytical method the main body of a book is made use of in second Zhang Zhong has studied the Smarandache function mean value character , has given a stronger asymptotic formula out and 2. The function has studied Smarandache having rich content , the mean value with the function of the figure that the Samarandache professor the main body of a book has been studied in third Zhang Zhong has brought forward, has given the concrete formula that mean value calculates with the function of figure out 3. And the go into about a little peculiar progression and the function mean value character has been very amusing , famous Fibonacci progression and Lucas progression have had the important effect in studying in mathematic theory , Zhang Zhong has studied the main body of a book in fourth being similar to peculiar progression counting function mean value this liang , has made use of elementary method to have reached a little new mean value formula, some character keyword of the progression having discussed broad wide Lucas: F.Smarandache problem , Smarandache function , number theory function , progression , counting function , mean value , asymptotic formula.
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热心网友时间：2024-12-03 22:36

Abstract
As everyone knows, the number-theoretic function of the mean estimate of number theory research in question occupies a very important position, and many well-known problem of number theory are closely related. And therefore in this area to make any substantive progress in number theory are bound to play an important development role in promoting! In this paper, the average number of Smarandache function and some question the nature of function. Function about the mean, this article studied the Smarandache function of the mean estimation problem, and has been about a better progressive; studied Samarandache Professor of the figure and function of the mean, and has been the number and function of the mean calculated specific formula; studied the Fibonacci series and Lucas series counting function of the mean, and give a mean value calculated on the counting function of some specific formula; the definition of a broad series of Lucas and Lucas to discuss a broad series of some properties. Specifically, the main results of this paper include the following:
1. Smarandache function to study the problem of the mean number theory occupies a very important position, it is lot of number-theoretic function is closely related to the mean. In this paper, in the second chapter and the use of elementary analytic method to study the nature of the mean value of Smarandache function and give a strong asymptotic formula.
2. Smarandache function is rich in content, this article in Chapter III to study the Samarandache Professor and function of the figure of the mean, give a figure and function of the specific formula for calculating the mean.
3. About some special function series and the nature of the study the mean is very interesting, well-known Fibonacci series and the Lucas series in the theory of mathematical research have an important role, this article in the fourth chapter to study these two types of special series counting function of the mean, using the elementary method to draw a number of new mean value formula, and Lucas to discuss a broad series of some properties.
Keywords: F. Smarandache problem, Smarandache function, number theory function, series, counting function, the mean, the asymptotic formula

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