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Displaying similar documents to “A generalisation of an identity of Lehmer”

Some finite generalizations of Euler's pentagonal number theorem

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.

Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies

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...

Low Mach number limit of a compressible Euler-Korteweg model

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.

The fundamental theorem of algebra before Carl Friedrich Gauss.

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,...

Fibonacci Numbers with the Lehmer Property

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

Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence

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.