On a conjecture of Erdös
W. Narkiewicz (1977)
Colloquium Mathematicae
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W. Narkiewicz (1977)
Colloquium Mathematicae
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Pandey, Ram Krishna (2009)
Journal of Integer Sequences [electronic only]
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Paule, Peter (1996)
Experimental Mathematics
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G. Grekos, L. Haddad, C. Helou, J. Pihko (2005)
Acta Arithmetica
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P. D. T. A. Elliott (1976)
Colloquium Mathematicae
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András Biró (2003)
Acta Arithmetica
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G. Besson (2009)
Bollettino dell'Unione Matematica Italiana
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K. Kubota (1977)
Acta Arithmetica
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K. Inkeri (1976)
Acta Arithmetica
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C. Greither, Radan Kučera (2008)
Acta Arithmetica
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Fuzhen Zhang (2016)
Special Matrices
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We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We...
Torossian, Charles (2002)
Journal of Lie Theory
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R. Dacić (1971)
Matematički Vesnik
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András Biró (2003)
Acta Arithmetica
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Sebastian Hebda (2013)
Colloquium Mathematicae
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We propose two conjectures which imply the Collatz conjecture. We give a numerical evidence for the second conjecture.
Shanta Laishram, T. N. Shorey (2012)
Acta Arithmetica
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Xiangneng Zeng, Yuanlin Li, Pingzhi Yuan (2015)
Acta Arithmetica
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Jean-Marc Deshouillers, Michael Drmota, Clemens Müllner (2015)
Studia Mathematica
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We prove that automatic sequences generated by synchronizing automata satisfy the full Sarnak conjecture. This is of particular interest, since Berlinkov proved recently that almost all automata are synchronizing.