13 papers
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…
On Even Perfect Numbers II
Hung Viet Chu
Let be a prime such that is a Mersenne prime. Let , where and is an odd prime. Continuing the work of Cai et al. and Jiang, w…
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}…
Representation of and
Hung Viet Chu
Let be relatively prime. We consider , which arises in the study of the -th cyclotomic polynomial, where are distinct primes. We prove…
When the Large Divisors of a Natural Number Are in Arithmetic Progression
Hung Viet Chu
Iannucci considered the positive divisors of a natural number that do not exceed the square root of and found all numbers whose such divisors are in arithmetic progression.…
A New Transcendental Number from
Hung Viet Chu
We first give a summary of the history of transcendental numbers then use a nice technique by G. Dresden to prove a new transcendental number. In particular, while previous work lo…