منابع مشابه
On power values of pyramidal numbers, I
For m ≥ 3, the mth order pyramidal number is defined by x(x + 1)((m−2)x+5−m)/6. These combinatorial numbers play an important role in number theory and discrete mathematics. For m = 3 and 4, all the power values of these polynomials have been already found. In the present paper the authors deal with square values for larger m. All integer solutions of the corresponding elliptic curves are given...
متن کاملGraphs with equal Independence and Annihilation Numbers
The annihilation number a of a graph is an upper bound of the independence number α of a graph. In this article we characterize graphs with equal independence and annihilation numbers. In particular, we show that α = a if, and only if, either (1) a ≥ n2 and α ′ = a, or (2) a < n2 and there is a vertex v ∈ V (G) such that α(G − v) = a(G), where α is the critical independence number of the graph....
متن کاملA characterization of trees with equal Roman 2-domination and Roman domination numbers
Given a graph $G=(V,E)$ and a vertex $v in V$, by $N(v)$ we represent the open neighbourhood of $v$. Let $f:Vrightarrow {0,1,2}$ be a function on $G$. The weight of $f$ is $omega(f)=sum_{vin V}f(v)$ and let $V_i={vin V colon f(v)=i}$, for $i=0,1,2$. The function $f$ is said to bebegin{itemize}item a Roman ${2}$-dominating function, if for every vertex $vin V_0$, $sum_{uin N(v)}f(u)geq 2$. The R...
متن کاملOn some polynomial values of repdigit numbers
We study the equal values of repdigit numbers and the k dimensional polygonal numbers. We state some effective finiteness theorems, and for small parameter values we completely solve the corresponding equations.
متن کاملThe Covering Numbers of Mycielski Ideals Are All Equal
The Mycielski ideal Mk is defined to consist of all sets A ⊆ k such that {f ↾ X : f ∈ A} 6= k for all X ∈ [ω]0 . It will be shown that the covering numbers for these ideals are all equal. However, the covering numbers of the closely associated Ros lanowski ideals will be shown to be consistently different.
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2018
ISSN: 0019-3577
DOI: 10.1016/j.indag.2018.01.010