本文選題：Smarandache　切入點(diǎn)：LCM函數(shù)　出處：《延安大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：摘要:Smarandache函數(shù)是數(shù)論研究的重要內(nèi)容之一,隨著人們對它的深入探索和研究,目前已經(jīng)出現(xiàn)了很多類函數(shù)方程和研究方法.本文在閱讀大量與Smarandache問題相關(guān)的書籍和文獻(xiàn)的基礎(chǔ)上,主要利用初等方法和解析方法對幾個(gè)Smarandache函數(shù)問題進(jìn)行研究,具體內(nèi)容如下:首先,研究了兩個(gè)包含Smarandache LCM函數(shù)方程S(SL(n)=(?)e(n)和Z(SL(n))=()?e(n)在e = 1,2時(shí)的可解性問題,給出了方程的所有正整數(shù)解;其次,研究了關(guān)于Smarandache LCM函數(shù)在簡單數(shù)序列上的均值性質(zhì),給出并證明了(?)和(?)的兩個(gè)漸近公式.并對SmarandacheLCM函數(shù)SL(n)與最大素因子函數(shù)之差的β次方的值分布問題和一個(gè)Smarandache可乘函數(shù)與最大素因子函數(shù)的β次混合均值問題進(jìn)行了探討研究,最終給出并證明了(?)(SL(n)-P(n))β和(?)(f(Pd(n))—1/2d(n)P(n))β的漸近公式;最后,研究了 Smarandache LCM函數(shù)SL(n)在特殊序列2p±1上的下界估計(jì)問題,給出并證明SL(2p±1)≥10p+1,其中素?cái)?shù)p≥17.
[Abstract]:The function of: Smarandache is one of the important contents in the study of number theory. With the deep exploration and research on it, there have been many kinds of functional equations and research methods. This paper mainly studies several Smarandache function problems by using elementary method and analytic method. The main contents are as follows: firstly, two Smarandache LCM function equations are studied. A) and a Zang SLN (a) and a sling (a) and a little bit (a)? In this paper, we give all positive integer solutions of the equation at e = 1, 2:00. Secondly, we study the mean value properties of Smarandache LCM functions on simple number sequences, and give and prove the results. ) and Ko? And the problem of the value distribution of the difference between the SmarandacheLCM function and the maximal prime factor function and the 尾 th mixed mean value problem of a Smarandache multiplicative function and the maximal prime factor function are studied. Finally, the author gives and proves the problem of the 尾 th order mixed mean value of the Smarandache multiplicative function and the maximal prime factor function. The 尾 and P??? Finally, the lower bound estimation problem of Smarandache LCM function on a special sequence 2p 鹵1 is studied, and it is proved that SL(2p 鹵1) 鈮，

本文編號：1602160