6 papers
On the quantity where is an odd perfect number -- Part II
Keneth Adrian Precillas Dagal, Jose Arnaldo Bebita Dris
In this note, we continue an approach pursued in an earlier paper of the second author and thereby attempt to produce an improved lower bound for the sum , where $…
Propagating Graceful Graphs and Trees
Keneth Adrian Dagal, Kristoffer Karan Hugo
In an attempt to prove the Graceful Tree Conjecture, we present two propagation of graphs. The first is to propagate graceful graphs, and the second is to propagate trees from a gr…
Sylvester's Conjecture and the Egyptian Fractions
Keneth Adrian Dagal
This paper attempts to prove the Sylvester's conjecture using Egyptian Fractions with two key ingredients. First, creating a set of operators that completely generates all possible…
Bounds for the Number of Terms of Harmonic Sums
Keneth Adrian Dagal
This paper provides bounds for the number of terms, denoted by , of a harmonic sum with the condition that it starts from any arbitrary unit fraction , , unt…
A New Operator for Egyptian Fractions
Keneth Adrian Dagal
This paper introduces a new equation for rewriting two unit fractions to another two unit fractions. This equation is useful for optimizing the elements of an Egyptian Fraction. Pa…
A Lower Bound for for -Multiperfect Number
Keneth Adrian Dagal
A natural number is said to be - multiperfect number if for some integer . In this paper, I will provide a lower bound for of any - multiper…