scholarly journals Domino Tiling Congruence Modulo 4

2009 ◽  
Vol 25 (4) ◽  
pp. 625-638 ◽  
Author(s):  
Bridget Eileen Tenner
Keyword(s):  
Domino Tiling ◽  
Congruence Modulo

A congruence for some generalized harmonic type sums

2018 ◽  
Vol 14 (04) ◽  
pp. 1033-1046 ◽  
Author(s):  
Haydar Göral ◽  
Doğa Can Sertbaş
Keyword(s):  
Harmonic Number ◽  
Congruence Modulo

In 1862, Wolstenholme proved that the numerator of the [Formula: see text]th harmonic number is divisible by [Formula: see text] for any prime [Formula: see text]. A variation of this theorem was shown by Alkan and Leudesdorf. Motivated by these results, we prove a congruence modulo some odd primes for some generalized harmonic type sums.

A NEW CONGRUENCE MODULO 25 FOR 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS

2014 ◽  
Vol 91 (1) ◽  
pp. 41-46 ◽  
Author(s):  
ERNEST X. W. XIA
Keyword(s):  
Positive Integer ◽  
Generating Function ◽  
Plane Partitions ◽  
Arithmetic Properties ◽  
Symmetric Plane ◽  
Congruence Modulo

AbstractFor any positive integer $n$, let $f(n)$ denote the number of 1-shell totally symmetric plane partitions of $n$. Recently, Hirschhorn and Sellers [‘Arithmetic properties of 1-shell totally symmetric plane partitions’, Bull. Aust. Math. Soc.89 (2014), 473–478] and Yao [‘New infinite families of congruences modulo 4 and 8 for 1-shell totally symmetric plane partitions’, Bull. Aust. Math. Soc.90 (2014), 37–46] proved a number of congruences satisfied by $f(n)$. In particular, Hirschhorn and Sellers proved that $f(10n+5)\equiv 0\ (\text{mod}\ 5)$. In this paper, we establish the generating function of $f(30n+25)$ and prove that $f(250n+125)\equiv 0\ (\text{mod\ 25}).$

On a Congruence modulo a Prime

2006 ◽  
Vol 113 (7) ◽  
pp. 652
Author(s):  
Hao Pan
Keyword(s):  
Congruence Modulo
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