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..., Shandong, P. R. China. Guo Jinbao, College of Mathematics and Computer Science, Yanan University, Yanan, Shaanxi, P. R. China. Copyright... ... their own articles Many books can be downloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherfor... ...articles Many books can be downloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ... .... Alexander Nathanson Mathematics is often referred to as a servant of science and number theory as a queen of mathematics, by which we are to un... ... to understand that number theory should contribute to the development of science by continuously supplying challenging problems and illustrative ex... ...hengdong and Pan Chengbiao. Foundation of Analytic Number Theory. Beijing: Sciencepress,1997. [4] Zhu Weiyi. On the k power complement and k power fre...

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...ewers: A. W. Vyawahare, H. O. D. Mathematics Department, M. M. College Of Science, Umred Road, Sakkardara, Nagpur University, Nagpur, PIN : - 44000... ...hit, H. O. D. Mathematics Department, V.M.V. Com., J.M.T. Arts & J.J.P. Science College, Wardhaman Nagar, Nagpur University, Nagpur, PIN : – 440008... ...enpeng, a nd A uthors . Many books one can download from the Digit al Library : http://www.gallup.unm.edu/~smarandache/eBooks - otherformats.htm... ...AND THE PRIMITIVE NUMBER OF POWER Zhang Wenpeng Research Center for Basic Science, Xi’an Jiaotong University, Xi’an, Shaanxi, P .R.China wpzhang@nwu.... ...TIVE NUMBERS OF POWER AND -POWER ROOTS Yi Yuan Research Center for Basic Science, Xi’an Jiaotong University, Xi’an, Shaanxi, P .R.China yiyuan74@163... ...rsity, Xi’an, Shaanxi, P .R.China yiyuan74@163.com Liang Fangchi School of Science, Air Force Engineering University, Xi’an, Shaanxi, P .R.China fc-li...

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...r residue of n 25 Li Junzhuang and Zhao Jian Generalization of the divisor products and proper divisor products sequences 29 Liang Fangchi The science of lucky sciences 33 Jon Perry Smarandache Sequence of Unhappy Numbers 37 Muneer Jebreel Karama On m -th power free part of an integer 39 Zhao Xiaopeng and Ren Zhibin On two new arithmetic functions and the k...

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...Charles Ashbacher Many books can be downloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherfor... ...bacher Many books can be downloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ... ...andache Partition Type and Other Sequences”, Bulletin of Pure and Applied Sciences, Vol. 16 E(No. 2) 1997, page 240. 12. Amarnath Murthy, “On The ...

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...la and Charles Ashbacher Many books can be downloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherform... ...les Ashbacher Many books can be downloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISB... ...DigitsInNumber%2; // If the input is less than one hundred, simply use the library functionality to // determine the square root. compareTest=theVal...

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...ry and geometry, is an ancient branch of mathematics. Number theory in mathematics position is special, Gauss once said: "Mathematics is the queen of sciences, number theory is the mathematics of the crown. "Although many of the problems in number theory began very early in the research, And has been fruitful, but there are still many of the mathematicians call "crown Ming...

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...llections at: the Arizona State University (Tempe, USA), Archives of American Mathematics (University of Texas at Austin, USA), University of Craiova Library (Romania), and Archives of State (Rm. Valcea, Romania). The Smarandache's universe is undoubtedly very fascinating and is halfway between the number theory and the recreational mathematics. Even though sometime this u...

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...n Mathematics (University of Texas at Austin, USA), University of Craiova Library (Romania), and Archives of State (Rm. Valcea, Romania). The Smarand... ...he Florentin Smarandache papers" special collection, University of Craiova Library, and Archivele Statului, Filiala Valcea) and another one (V) to the... ...tillo, Smarandache continued fractions, Bulletin of pure and applied Sciences, Vol. 17E, No.1, 1998, p. 149-151 [6] F. Russo, Some results about... ...tillo, Smarandache continued fractions, Bulletin of pure and applied Sciences, Vol. 17E, No.1, 1998, p. 149-151 [4] F. Russo, Some results about... ...tillo, Smarandache continued fractions, Bulletin of pure and applied Sciences, Vol. 17E, No.1, 1998, p. 149-151 [3] F. Russo, Some results about... ...andache papers" special collection, Arizona State University, Hayden Library, Tempe, Box 871006, AZ 85287- 1006, USA; [3] C. Dumitrescu and... ... Generalize Andrica's Conjecture", Arizona State University, Hayden Library, Special Collections, Tempe, AZ, USA. [2] http://www.gallup.u... ....edu/~smarandache/russo3.htm [3] M. Bencze, Bulletin of Pure and Applied Sciences. Vol. 17 E(No. 1) 1998; p. 55-62 [4] http://www.gallup... ...illo, Smarandache continued fractions, Bulletin of pure and applied Sciences, Vol. 17E, No.1, 1998, p. 149-151 [13] S. Finch in http://www.math...

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................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using SuperMathematics Circular Ex-Centric Functions, by Florentin Smarandache & Mircea Eugen..........................

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................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using SuperMathematics Circular Ex-Centric Functions, by Florentin Smarandache & Mircea Eugen..........................