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Construction of Šindel sequences

Michal Křížek, Alena Šolcová, Lawrence Somer (2007)

Commentationes Mathematicae Universitatis Carolinae

We found that there is a remarkable relationship between the triangular numbers T k and the astronomical clock (horologe) of Prague. We introduce Šindel sequences { a i } ⊂ ℕ of natural numbers as those periodic sequences with period p that satisfy the following condition: for any k ∈ ℕ there exists n ∈ ℕ such that T k = a 1 + ⋯ + a n . We shall see that this condition guarantees a functioning of the bellworks, which is controlled by the horologe. We give a necessary and sufficient condition for a periodic sequence to be a Šindel sequence....

Corrigendum to “Congruences for certain binomial sums”

Jung-Jo Lee (2013)

Czechoslovak Mathematical Journal

Theorem 1 of J.-J. Lee, Congruences for certain binomial sums. Czech. Math. J. 63 (2013), 65–71, is incorrect as it stands. We correct this here. The final result is changed, but the essential idea of above mentioned paper remains valid.

Criteria for testing Wall's question

Jiří Klaška (2008)

Czechoslovak Mathematical Journal

In this paper we find certain equivalent formulations of Wall's question and derive two interesting criteria that can be used to resolve this question for particular primes.

Curiosité mathématique

G. Tarry (1899)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Distribution of quadratic non-residues which are not primitive roots

S. Gun, B. Ramakrishnan, Binod Kumar Sahoo, Ravindranathan Thangadurai (2005)

Mathematica Bohemica

In this article we study, using elementary and combinatorial methods, the distribution of quadratic non-residues which are not primitive roots modulo p h or 2 p h for an odd prime p and h ≥ 1 an integer.

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