Periodica. Math.
58(2009), 123
Sylvain Col 
Abstract. Les propriétés multiplicatives des nombres ellipséphiques peuvent {\accent 94 e}tre obtenues {\accent 18 a} l'aide des moments de la série génératrice de cette suite. Nous donnons des estimations précises pour les grands moments par deux méthodes distinctes : l'une combinatoire fournit un résultat précis dans le cas réputé le plus difficile des nombres n'utilisant que les $0$ et les $1$ ; la seconde purement analytique fournit un résultat sans condition sur les chiffres.
Periodica. Math.
58(2009), 2534
Eszter K. Horváth  ,  Zoltán Németh 

Gabriella Pluhár 
Abstract. The aim of the present paper is to carry on the research of Czédli in determining the maximum number of rectangular islands on a rectangular grid. We estimate the maximum of the number of triangular islands on a triangular grid.
Periodica. Math.
58(2009), 3545
Attila Bérczes 

István Járási 
Abstract. We investigate the possibility of using index forms as basic ingredients of cryptographically important functions. We suggest the use of a hash function based on index forms and we prove some important properties of the suggested function.
Periodica. Math.
58(2009), 4758
Mario Huicochea 

Jesús JerónimoCastro  2 
Abstract. In this paper the following is proved: let ${\cal P}$ be a centrally symmetric set of points, such that the distance between any pair of points is at least $1$ and every three of them can be covered by a strip of width $1$. Then there is a strip of width $\radical "270370 {2}$ covering ${\cal P}.$
2  Supported by CONACYT, SNI 38848 
Periodica. Math.
58(2009), 5970
Bo He 

Alain Togbé 
Abstract. We prove that if $k$ is a positive integer and $d$ is a positive integer such that the product of any two distinct elements of the set $ \delimiter "4266308 k+1,4k,9k+3,d\delimiter "5267309 $ increased by $1$ is a perfect square, then $d=144k^3 + 192k^2 + 76k+ 8$.
Periodica. Math.
58(2009), 7182
Horst Alzer 

Stamatis Koumandos 
Abstract. We present several series and product representations for $\gamma $, $\pi $, and other mathematical constants. One of our results states that we have for all real numbers $\mu >0$: $$ \gamma = \sum _{k=0}^{\infty }{1\over (1+\mu )^{k+1}} \sum _{m=0}^k{k \atopwithdelims ()m}(1)^m {\mu }^{km}S(m),$$ where $S(m)=\sum _{k=1}^{\infty }{1\over 2^k+m}$.
Periodica. Math.
58(2009), 8398
Tünde Kovács 
Abstract. We give several effective and explicit results concerning the values of some polynomials in binary recurrence sequences. First we provide an effective finiteness theorem for certain combinatorial numbers (binomial coefficients, products of consecutive integers, power sums, alternating power sums) in binary recurrence sequences, under some assumptions. We also give an efficient algorithm (based on genus 1 curves) for determining the values of certain degree 4 polynomials in such sequences. Finally, partly by the help of this algorithm we completely determine all combinatorial numbers of the above type for the small values of the parameter involved in the Fibonacci, Lucas, Pell and associated Pell sequences.
Periodica. Math.
58(2009), 99119
Katalin Gyarmati  1 
Abstract. In the applications it may occur that our initial pseudorandom binary sequence turns out to be not long enough, thus we have to take the concatenation or merging of it with another pseudorandom binary sequences. Here our goal is study when can we form the concatenation of several pseudorandom binary sequences belonging to a given family? We introduce and study new measures which can be used for answering this question.
1  Research partially supported by Hungarian NFSR, Grants No. K49693, K67676, K72264 and the János Bolyai Research Fellowship. 
Periodica. Math.
58(2009), 121126
Hiroshi Maehara  1  ,  Imre Z.\ Ruzsa  2 

Norihide Tokushige  3 
Abstract. We prove that the $n$dimensional unit hypercube contains an $n$dimensional regular simplex of edge length $c\radical "270370 {n}$, where $c>0$ is a constant independent of $n$.
1  Supported by MEXT GrantinAid for Scientific Research (B) 20340022.  
2  Supported by Hungarian NFSR (OTKA), grants No. K 61908, K 72731.  
3  Supported by MEXT GrantinAid for Scientific Research (B) 20340022. 