On the congruence xn + yn + zn ... 0 (mod p).

L.E. Dickson

Displaying similar documents to “On the congruence xn + yn + zn ... 0 (mod p).”

Congruence properties of the number of solutions of some equations.

S. Chowla, J. Cowles, M. Cowles (1978)

Journal für die reine und angewandte Mathematik

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Partitioning multipartite numbers into a fixed number of parts which satisfy congruence conditions.

M.M. Robertson (1977)

Journal für die reine und angewandte Mathematik

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Unboundedness results for systems

Gabriel Lugo, Frank Palladino (2009)

Open Mathematics

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We study k th order systems of two rational difference equations $x_{n} = \frac{α + \sum_{i = 1}^{k} β_{i} x_{n - i} + \sum_{i = 1}^{k} γ_{i} y_{n - i}}{A + \sum_{j = 1}^{k} B_{j} x_{n - j} + \sum_{j = 1}^{k} C_{j} y_{n - j}}, n \in ℕ,$ In particular we assume non-negative parameters and non-negative initial conditions. We develop several approaches which allow us to prove that unbounded solutions exist for certain initial conditions in a range of the parameters.

Multiplicative even functions (mod r). I Structural properties.

R. Sivaramakrishnan (1978)

Journal für die reine und angewandte Mathematik

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One tripled fixed point result in partially ordered 0-complete partial metric spaces

Miloje Rajović, Jelena Vujaković, Milena Lekić (2013)

Kragujevac Journal of Mathematics

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On congruence conditions for primality.

Gong, Sherry, Kominers, Scott Duke (2010)

Integers

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On the nonvanishing of Fermat quotients (mod p).

Wells Johnson (1977)

Journal für die reine und angewandte Mathematik

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On the congruence f(x) + g(y) + c ≡ 0 (mod xy) (completion of Mordell's proof)

A. Schinzel (2015)

Acta Arithmetica

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Assertions on the congruence f(x) + g(y) + c ≡ 0 (mod xy) made without proof by Mordell in his paper in Acta Math. 88 (1952) are either proved or disproved.

Some boundedness results for systems of two rational difference equations

Gabriel Lugo, Frank Palladino (2010)

Open Mathematics

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We study k th order systems of two rational difference equations $x_{n} = \frac{α + \sum_{i = 1}^{k} β_{i} x_{n - 1} + \sum_{i = 1}^{k} γ_{i} y_{n - 1}}{A + \sum_{j = 1}^{k} B_{j} x_{n - j} + \sum_{j = 1}^{k} C_{j} y_{n - j}}, y_{n} = \frac{p + \sum_{i = 1}^{k} δ_{i} x_{n - i} + \sum_{i = 1}^{k} ε_{i} y_{n - i}}{q + \sum_{j = 1}^{k} D_{j} x_{n - j} + \sum_{j = 1}^{k} E_{j} y_{n - j}} n \in ℕ$ . In particular, we assume non-negative parameters and non-negative initial conditions, such that the denominators are nonzero. We develop several approaches which allow us to extend well known boundedness results on the k th order rational difference equation to the setting of systems in certain cases.