Excedance numbers for permutations in complex reflection groups.
Mansour, Toufik, Sun, Yidong (2007)
Séminaire Lotharingien de Combinatoire [electronic only]
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Mansour, Toufik, Sun, Yidong (2007)
Séminaire Lotharingien de Combinatoire [electronic only]
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Bagno, Eli, Garber, David (2005)
Séminaire Lotharingien de Combinatoire [electronic only]
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Lewittes, Joseph, Kolyvagin, Victor (2010)
The New York Journal of Mathematics [electronic only]
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Mansour, Toufik (2001)
Séminaire Lotharingien de Combinatoire [electronic only]
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Zhi-Wei Sun (1992)
Acta Arithmetica
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Let Fₙ be the Fibonacci sequence defined by F₀=0, F₁=1, . It is well known that for any odd prime p, where (-) denotes the Legendre symbol. In 1960 D. D. Wall [13] asked whether is always impossible; up to now this is still open. In this paper the sum is expressed in terms of Fibonacci numbers. As applications we obtain a new formula for the Fibonacci quotient and a criterion for the relation (if p ≡ 1 (mod 4), where p ≠ 5 is an odd prime. We also prove that the affirmative...
Lomadze, G. (2001)
Georgian Mathematical Journal
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J. Browkin, A. Schinzel (1995)
Colloquium Mathematicae
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W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers (k = 1, 2,...) is of the form n - φ(n).
J. H. E. Cohn (1992)
Acta Arithmetica
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Fethi Ben Saïd, Jean-Louis Nicolas, Ahlem Zekraoui (2010)
Journal de Théorie des Nombres de Bordeaux
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Improving on some results of J.-L. Nicolas [], the elements of the set , for which the partition function (i.e. the number of partitions of with parts in ) is even for all are determined. An asymptotic estimate to the counting function of this set is also given.
Szymanski, Artur, Wojda, A.Paweł (2010)
The Electronic Journal of Combinatorics [electronic only]
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