發(fā)布時間：2018-06-27 01:18

  本文選題：不定方程 + 數(shù)論函數(shù)��； 參考：《西安工程大學(xué)》2016年碩士論文

【摘要】：對不定方程的研究一直是人們關(guān)注的課題,尤其是有關(guān)數(shù)論函數(shù)的不定方程.許多專家和學(xué)者對這些問題進(jìn)行了深入的研究和探索,得到了很多有意義的研究成果.本文利用初等數(shù)論方法研究了一些包含特殊整數(shù)數(shù)列和數(shù)論函數(shù)的不定方程,得到了它們的一些正整數(shù)解.首先,討論與Smarandache原函數(shù)和特殊數(shù)列有關(guān)的不定方程的可解性,將Smarandache原函數(shù)與三角形數(shù),五邊形數(shù)分別結(jié)合,得到兩個不定方程,利用初等數(shù)論方法得到方程所有的正整數(shù)解.其次,討論與Pell數(shù)列和數(shù)論函數(shù)有關(guān)的不定方程的可解性,將Euler函數(shù),因子求和函數(shù),Smarandache函數(shù)與Pell數(shù)列,Pell-Lucas數(shù)列結(jié)合,得到一系列不定方程,利用初等數(shù)論方法和Pell數(shù)列以及Pell-Lucas數(shù)列的性質(zhì),得到相關(guān)結(jié)論.再次,運用初等數(shù)論方法證明不定方程x~3-5~3=3py~2有適合gcd(x,y)=1的正整數(shù)解的充要條件.最后,總結(jié)本文關(guān)于數(shù)論函數(shù)以及特殊數(shù)列的不定方程求解,并提出可以進(jìn)一步研究的問題
[Abstract]:The study of the indeterminate equation has been a subject of concern, especially the indeterminate equation of the number theory function. Many experts and scholars have studied and explored these problems deeply, and got a lot of meaningful research results. In this paper, some special integer numbers and number theory functions are studied by means of elementary number theory. Some positive integer solutions of the equation are obtained. First, the solvability of the indefinite equations related to the Smarandache original function and the special series is discussed. Two indeterminate equations are obtained by combining the Smarandache original function with the triangle number and the pentagon number respectively, and all the positive integer solutions of the equation are obtained by the elementary number theory. Secondly, the discussion and Pell are discussed. The solvability of the indefinite equations related to the number of series and the number theory function, the Euler function, the factor summation function, the Smarandache function and the Pell series and the Pell-Lucas series are combined to obtain a series of indeterminate equations, and the relevant conclusions are obtained by using the elementary number theory method and the properties of the Pell series and the Pell-Lucas series. Thirdly, the method of elementary number is used to prove that no The definite equation x~3-5~3=3py~2 has a sufficient and necessary condition for the positive integer solution suitable for GCD (x, y) =1. Finally, the solution of the indefinite equation of the number theory function and the special series is summed up, and the problems that can be further studied are put forward.
【學(xué)位授予單位】：西安工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O156

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 朱敏慧;張娟娟;崔艷;;方程x~3-1=2py~2有正整數(shù)解的判別條件[J];內(nèi)蒙古師范大學(xué)學(xué)報(自然科學(xué)漢文版);2014年04期

2 杜先存;劉玉鳳;管訓(xùn)貴;;關(guān)于丟番圖方程x~3±5~3=3py~2[J];沈陽大學(xué)學(xué)報(自然科學(xué)版);2014年01期

3 廖軍;普粉麗;;關(guān)于丟番圖方程x~3-27=Dy~2[J];西安文理學(xué)院學(xué)報(自然科學(xué)版);2014年01期

4 錢立凱;普粉麗;;關(guān)于不定方程x~3±64=Dy~2的整數(shù)解[J];西安文理學(xué)院學(xué)報(自然科學(xué)版);2014年01期

5 普粉麗;杜先存;;關(guān)于不定方程x~3±5~3=3Dy~2[J];海南大學(xué)學(xué)報(自然科學(xué)版);2013年04期

6 管訓(xùn)貴;杜先存;;關(guān)于Diophantine方程x~3±1=pqy~2[J];安徽大學(xué)學(xué)報(自然科學(xué)版);2014年01期

7 錢立凱;;不定方程x~3±1=Dy~2解的研究[J];曲靖師范學(xué)院學(xué)報;2013年06期

8 王婷婷;;Fibonacci數(shù)列倒數(shù)的無窮和[J];數(shù)學(xué)學(xué)報;2012年03期

9 張文鵬;王婷婷;;Pell數(shù)平方倒數(shù)的無限和(英文)[J];渭南師范學(xué)院學(xué)報;2011年10期

10 楊雅琳;;Diophantine方程x~3-8=py~2解的研究[J];紡織高�；A(chǔ)科學(xué)學(xué)報;2010年03期

相關(guān)博士學(xué)位論文 前1條

1 陳德溢;數(shù)論中的若干問題[D];浙江大學(xué);2014年

，

本文編號：2072123