H. Chu

activity

20162023

most citedGeneralizations of a Curious Family of MSTD Sets Hidden By Interior Blocks

4 citations · 15 across the 40 of their papers we have counts for

collaborators

Showing 2020Show all

11 papers · 1 filter

math.NT2020

Difference in the Number of Summands in the Zeckendorf Partitions of Consecutive Integers

Hung Viet Chu

Zeckendorf proved that every positive integer has a unique partition as a sum of non-consecutive Fibonacci numbers. We study the difference between the number of summands in the pa…

math.HO2020

Visualize Geometric Series

Hung Viet Chu

We review Mabry's, Edgar's, and the Viewpoints 2000 Group's proofs without words for the geometric series formula. Mabry and Edgar proved without words that $$\frac{1}{4} + \left(\…

math.NT2020

On Generalized Zeckendorf Decompositions and Generalized Golden Strings

Hung Viet Chu

Zeckendorf proved that every positive integer has a unique representation as a sum of non-consecutive Fibonacci numbers. A natural generalization of this theorem is to look at the…

math.CO2020

Various Sequences from Counting Subsets

Hung Viet Chu

We count the number of subsets of ${1, 2, \dots, n}$ under different conditions and study the sequence obtained as we let $n$ increase.

math.NT2020

Generalizing the Distribution of Missing Sums in Sumsets

Hung V. Chu, Dylan King, Noah Luntzlara +5

Given a finite set of integers $A$ , its sumset is $A + A := {a_{i} + a_{j} ∣ a_{i}, a_{j} \in A}$ . We examine $∣ A + A ∣$ as a random variable, where $A \subset I_{n} = [0, n - 1]$ , the set of integer…

math.NT2020★ 1 cited

On Zeckendorf Related Partitions Using the Lucas Sequence

Hung V. Chu, David C. Luo, Steven J. Miller

Zeckendorf proved that every positive integer has a unique partition as a sum of non-consecutive Fibonacci numbers. Similarly, every natural number can be partitioned into a sum of…

math.NT2020

On Even Perfect Numbers II

Hung Viet Chu

Let $k > 2$ be a prime such that $2^{k} - 1$ is a Mersenne prime. Let $n = 2^{α - 1} p$ , where $α > 1$ and $p < 3 \cdot 2^{α - 1} - 1$ is an odd prime. Continuing the work of Cai et al. and Jiang, w…

math.NT2020

A Twist of a Ramanujan Identity

Hung Viet Chu, Lan Khanh Chu

Ramanujan wrote the following identity \begin{align*} \sqrt{2 \left(1 - \frac{1}{3^2}\right) \left(1 - \frac{1}{7^2}\right) \left(1 - \frac{1}{11^2}\right) \left(1 - \frac{1}{19^2}…

math.NT2020

Representation of $\frac{1}{2} (F_{n} - 1) (F_{n + 1} - 1)$ and $\frac{1}{2} (F_{n} - 1) (F_{n + 2} - 1)$

Hung Viet Chu

Let $a, b \in N$ be relatively prime. We consider $(a - 1) (b - 1) /2$ , which arises in the study of the $pq$ -th cyclotomic polynomial, where $p, q$ are distinct primes. We prove…

math.NT2020

When the Nontrivial, Small Divisors of a Natural Number are in Arithmetic Progression

Hung Viet Chu

Iannucci considered the positive divisors of a natural number $n$ that do not exceed $n$ and found all forms of numbers whose such divisors are in arithmetic progression. In…

math.NT2020

On Arithmetic Progressions of Powers in Cyclotomic Polynomials

Hung Viet Chu

We determine necessary conditions for when powers corresponding to positive/negative coefficients of $Φ_{n}$ are in arithmetic progression. When $n = pq$ for any primes $q > p > 2$ , ou…

Difference in the Number of Summands in the Zeckendorf Partitions of Consecutive Integers

Visualize Geometric Series

On Generalized Zeckendorf Decompositions and Generalized Golden Strings

Various Sequences from Counting Subsets

Generalizing the Distribution of Missing Sums in Sumsets

On Zeckendorf Related Partitions Using the Lucas Sequence

On Even Perfect Numbers II

A Twist of a Ramanujan Identity

Representation of 21​(Fn​−1)(Fn+1​−1) and 21​(Fn​−1)(Fn+2​−1)

When the Nontrivial, Small Divisors of a Natural Number are in Arithmetic Progression

On Arithmetic Progressions of Powers in Cyclotomic Polynomials

Representation of $\frac{1}{2} (F_{n} - 1) (F_{n + 1} - 1)$ and $\frac{1}{2} (F_{n} - 1) (F_{n + 2} - 1)$