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Dynamic Balance: A Thermodynamic Principle for the Emergence of the Golden Ratio in Open Non-Equilibrium Steady States. [PDF]
Entropy (Basel)Ruiz A.
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Message-Passing Monte Carlo: Generating low-discrepancy point sets via graph neural networks. [PDF]
Proc Natl Acad Sci U S ARusch TK +4 more
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Factorization of Fibonacci Numbers
The Fibonacci Quarterly, 1970The Fibonacci numbers \(F_n\) may be defined by \(F_0 = 0\), \(F_1= 1\), \(F_{n+1}=F_n +F_{n-1}\) for \(n \geq 1\). If \(F_z\) \(z>0\), is the smallest Fibonacci number divisible by the prime \(p\), then \(z =a(p)\) is defined as the entry point (or rank) of \(p\); moreover \(p\) divides \(F_n\) if and only if \(n\) is divisible by \(z(p)\).
Daykin, D. E., Dresel, L. A. G.
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The College Mathematics Journal, 2008
Ezra (Bud) Brown (ezbrown@math.vt.edu) grew up in New Orleans and has degrees from Rice and LSU. He arrived at Virginia Tech shortly after Hurricane Camille, and has been there ever since, with time out for sabbatical visits to Washington, DC (where he has spent his summers since 1993) and Munich.
Ezra Brown, Jason C. Brunson
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Ezra (Bud) Brown (ezbrown@math.vt.edu) grew up in New Orleans and has degrees from Rice and LSU. He arrived at Virginia Tech shortly after Hurricane Camille, and has been there ever since, with time out for sabbatical visits to Washington, DC (where he has spent his summers since 1993) and Munich.
Ezra Brown, Jason C. Brunson
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Abstract The Fibonacci numbers are introduced and carefully developed together with a bit of biography of Fibonacci himself. He is best known for promoting the use of Hindu-Arabic numerals in Europe and especially for his “rabbit problem” which introduces the Fibonacci numbers. Of special interest is the decimal expansion for 1/89 having
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The American Mathematical Monthly, 1961
where I=2(p-qb), m=2(p-gqa), a= l (1 + \15), b-(1-\/5). The purpose of this article is to find a connection between generalized Fibonacci numbers and Pythagorean number triples. By a Pythagorean (number) triple is meant a set of three mutually prime integers u, v, w for which u2+v2 = w2.
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where I=2(p-qb), m=2(p-gqa), a= l (1 + \15), b-(1-\/5). The purpose of this article is to find a connection between generalized Fibonacci numbers and Pythagorean number triples. By a Pythagorean (number) triple is meant a set of three mutually prime integers u, v, w for which u2+v2 = w2.
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Cancer treatment and survivorship statistics, 2022
Ca-A Cancer Journal for Clinicians, 2022Kimberly D Miller +2 more
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