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Vol.2 The Academic Canon of Arts and Humanities, and Science >

Please use this identifier to cite or link to this item: http://hdl.handle.net/11266/6646

Title: The abc Conjecture of the Derived Logarithmic Functions of Euler’s Function and Its Computer Verification
Authors: Yamashita, Michinori
Miyata, Daisuke
Fujita, Natsumi
山下, 倫範
宮田, 大輔
藤田, 菜摘
Issue Date: 20-Mar-2019
Publisher: Rissho University
Abstract: Regarding Euler’s (totient) function, for an arbitrary number n > 1, there exists a k that possesses the characteristic where φk (n) = 1. In this case, if k is expressed as L(n) for n, then L possesses the characteristic of being perfectly logarithmic. For this L, we (Yamashita, Miyata) have provided the following L version abc conjecture. Conjecture: When a, b, and c are relatively prime, numbers are natural, and a + b = c, then max{L(a), L(b), L(c)} < 2∙L(rad (abc)) is feasible. This paper describes the properties of L and presents verification that this conjecture is correct up to 109 using a computer experiment. We also note that the abc conjecture recently considered solved by Prof. Mochizuki at Kyoto University is different from the conjecture presented here.
URI: http://hdl.handle.net/11266/6646
ISBN: 9784582474428
Appears in Collections:Vol.2 The Academic Canon of Arts and Humanities, and Science

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