相似结构的非线性:On (3a−1)(3b−1)= (5c−1)(5d−1)，且gu=fv。

viXra Pub Date : 2020-06-01 DOI:10.2139/ssrn.3566925

Michael C. I. Nwogugu

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摘要

Liptai, Nemeth等人(2020)推测(并假定证明)在正整数a≤b, c≤d的丢芬图方程(3a−1)(3b−1)=(5c−1)(5d−1)中，标题方程的唯一解是(a,b,c,d)=(1,2,1,1)。本文证明了Liptai, Nemeth, et. al.(2020)猜想和结果是错误的，方程(3a−1)(3b−1)=(5c−1)(5d−1)存在不止一个解。本文介绍了“存在条件”和“理性等价”的新理论，以及关于方程gu=fv的一个新定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Nonlinearity In Similar Structures: On (3a−1)(3b−1) = (5c−1)(5d−1), And gu=fv.

Liptai, Nemeth, et. al. (2020) conjectured (and supposedly proved) that in the diophantine equation (3a−1)(3b−1)=(5c−1)(5d−1) in positive integers a≤b, and c≤d, the only solution to the title equation is (a,b,c,d)=(1,2,1,1). This article proves that the Liptai, Nemeth, et. al. (2020) conjecture and results are wrong, and that there is more than one solution for the equation (3a−1)(3b−1)=(5c−1)(5d−1). This article introduces “Existence Conditions” and new theories of “Rational Equivalence”, and a new theorem pertaining to the equation gu=fv.

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