On the congruence f(x) + g(y) + c ≡ 0 (mod xy)
A. Schinzel (2016)
Banach Center Publications
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Four theorems of the author on the subject are given without proofs.
A. Schinzel (2016)
Banach Center Publications
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Four theorems of the author on the subject are given without proofs.
Gong, Sherry, Kominers, Scott Duke (2010)
Integers
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Scott Ahlgren (2003)
Acta Arithmetica
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William Y. C. Chen, Ernest X. W. Xia (2014)
Acta Arithmetica
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Let p̅(n) denote the number of overpartitions of n. It was conjectured by Hirschhorn and Sellers that p̅(40n+35) ≡ 0 (mod 40) for n ≥ 0. Employing 2-dissection formulas of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for p̅(40n+35) modulo 5. Using the (p, k)-parametrization of theta functions given by Alaca, Alaca and Williams, we prove the congruence p̅(40n+35) ≡ 0 (mod 5) for n ≥ 0. Combining this congruence and the congruence p̅(4n+3)...
Manfred Armbrust (1973)
Colloquium Mathematicae
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Marica D. Prešić (1979)
Publications de l'Institut Mathématique
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Hao Pan (2007)
Acta Arithmetica
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Ivan Chajda, Radomír Halaš (2002)
Discussiones Mathematicae - General Algebra and Applications
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We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.
Ying Zhang (2007)
Acta Arithmetica
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Magill, K.D.jun. (1984)
International Journal of Mathematics and Mathematical Sciences
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Gábor Czédli, Eszter K. Horváth (2002)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Gerhard Dorfer (2001)
Discussiones Mathematicae - General Algebra and Applications
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In this paper congruences on orthomodular lattices are studied with particular regard to analogies in Boolean algebras. For this reason the lattice of p-ideals (corresponding to the congruence lattice) and the interplay between congruence classes is investigated. From the results adduced there, congruence regularity, uniformity and permutability for orthomodular lattices can be derived easily.
John H. Hodges (1966)
Mathematische Zeitschrift
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E. Nazarewicz, M. O'Brien, M. O'Neill, C. Staples (2007)
Acta Arithmetica
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Ivan Chajda, Günther Eigenthaler (2001)
Discussiones Mathematicae - General Algebra and Applications
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It is well known that every congruence regular variety is n-permutable (in the sense of [9]) for some n ≥ 2. For the explicit proof see e.g. [2]. The connections between this n and Mal'cev type characterizations of congruence regularity were studied by G.D. Barbour and J.G. Raftery [1]. The concept of local congruence regularity was introduced in [3]. A common generalization of congruence regularity and local congruence regularity was given in [6] under the name "dual congruence regularity...
Xu, Ping, Pan, Hao (2007)
Integers
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