Linear equations with the Euler totient function
Florian Luca, Pantelimon Stănică (2007)
Acta Arithmetica
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Florian Luca, Pantelimon Stănică (2007)
Acta Arithmetica
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Tasoev, B.G. (1999)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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William D. Banks, Florian Luca (2005)
Acta Arithmetica
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Hao Pan, Zhi-Wei Sun (2006)
Acta Arithmetica
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William D. Banks, John B. Friedlander, Florian Luca, Francesco Pappalardi, Igor E. Shparlinski (2006)
Acta Arithmetica
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Ji-Cai Liu (2017)
Czechoslovak Mathematical Journal
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Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem.
Sz. Tengely (2008)
Acta Arithmetica
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Hirotaka Akatsuka (2006)
Acta Arithmetica
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Hoang Ngoc Minh, Jacob, Gérad, Petitot, Michel, Oussous, Nour Eddine (1999)
Séminaire Lotharingien de Combinatoire [electronic only]
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Ken Shirakawa (2009)
Banach Center Publications
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In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of...
Yajie Wang, Jianwei Yang (2023)
Applications of Mathematics
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This article deals with the low Mach number limit of the compressible Euler-Korteweg equations. It is justified rigorously that solutions of the compressible Euler-Korteweg equations converge to those of the incompressible Euler equations as the Mach number tends to zero. Furthermore, the desired convergence rates are also obtained.
Miloš Čanak (1994)
Matematički Vesnik
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Światosław R. Gal (2001)
Colloquium Mathematicae
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A closed form formula (generating function) for the Euler characteristic of the configuration space of n particles in a simplicial complex is given.
Josep Pla i Carrera (1992)
Publicacions Matemàtiques
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This is a paper about the first attemps of demonstration of the fundamental theorem of algebra. Before, we analyze the tie between complex numbers and the number of roots of an equation of n-th degree. In the second paragraph, we see the relation between integration and the fundamental theorem. Finally, we observe the linear differential equation with constant coefficients and Euler's position about the fundamental theorem, and then we consider d'Alembert's,...
Kevin Broughan, Kevin Ford, Florian Luca (2013)
Colloquium Mathematicae
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If n is a positive integer such that ϕ(n)σ(n) = m² for some positive integer m, then m ≤ n. We put m = n-a and we study the positive integers a arising in this way.
Kevin Ford, Yong Hu (2008)
Acta Arithmetica
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A. R. Sarpe (1972)
Matematički Vesnik
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Florian Luca (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show that if m > 1 is a Fibonacci number such that ϕ(m) | m-1, where ϕ is the Euler function, then m is prime
Zhi-Wei Sun, Hao Pan (2006)
Acta Arithmetica
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István Mező, Ayhan Dil (2009)
Open Mathematics
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In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization of Gosper’s identity. A classification of second order recurrence sequences is also given with the help of this method.
Kim, T., Kim, Y.H. (2010)
Journal of Inequalities and Applications [electronic only]
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Ryoo, C.S., Kim, T., Jang, Lee-Chae (2007)
Journal of Inequalities and Applications [electronic only]
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