algorithm-for-pollock-s-icosahedral-and-dodecahedral-numbers-conjectures
Science Score: 44.0%
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Low similarity (5.1%) to scientific vocabulary
Repository
Basic Info
- Host: GitHub
- Owner: Anjisweety2
- Language: Python
- Default Branch: main
- Size: 188 KB
Statistics
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 0
Metadata Files
README.md
"Python algorithm.py" file description
Based on our modified Pollock's conjectures, the functions test whether every positive integer in some given range can be written as a sum of at most: - 15 icosahedral numbers - 22 dodecahedral numbers The expected output is an empty set, which means that there are no positive integers in the given range that CANNOT be written as a sum of 15 icosahedral numbers, or 22 dodecahedral numbers. The actual output confirms that this statement is true.
"Detailed Proof of Thm 1.3 and 1.4.pdf" file description
This file contains a detailed explanation of the steps to complete the proofs of Theorem 1.3 and 1.4 in the paper (citation: Debmalya Basak, Anji Dong, Katerina Saettone, and Alexandru Zaharescu. Pollock’s Conjectures on Icosahedral and Dodecahedral Numbers. Preprint. 2024.).
To be precise, using previous results in the paper, "Proof of Theorem 1.3" and "Proof of Theorem 1.4" solve the problems of writing numbers less than $9.6446 \times 10^{35}$ as a sum of at most 15 icosahedral numbers and writing numbers less than $5.04 \times 10^{38}$ as a sum of at most 22 dodecahedral numbers respectively.
Owner
- Login: Anjisweety2
- Kind: user
- Repositories: 1
- Profile: https://github.com/Anjisweety2
Citation (CITATION.cff)
cff-version: 1.2.0 message: "If you use this algorithm, please cite it as below." author: - Anji Dong title: "Algorithm for Pollock's icosahedral and dodecahedral numbers conjectures" date-released: 2024-06-10