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Linear recurrences of order at most two in nontrivial small divisors and large divisors
Hung Viet Chu, Kevin Huu Le, Steven J. Miller +2
For each positive integer , define $$S'_N \ =\ \{1 < d < \sqrt{N}: d|N\}\mbox{ and }L'_N \ =\ \{\sqrt{N} < d < N : d|N\}.$$ Recently, Chentouf characterized all positive integer…
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…
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…