SciTech-Mathmatics-UNIQUE FACTORIZATION THEOREM + Science Hackathon Prizes@Kaggle.com
SciTech-Mathmatics-UNIQUE FACTORIZATION THEOREM
https://brilliant.org/wiki/fundamental-theorem-of-arithmetic/
Elementary_Number_Theory:
https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_(Clark)/01%3A_Chapters/1.11%3A_Unique_Factorization
https://public.csusm.edu/aitken_html/m422/Handout2.pdf
https://www.oxfordreference.com/display/10.1093/oi/authority.20110803110719647
UNIQUE FACTORIZATION THEOREM
In general, Every integer \(\large n > 1\) can be written UNIQUELY in the form:
\(\large \begin{array}{ccl} n &=& P_{1}^{a_1} \cdot P_{1}^{a_1} \cdot ... \cdot P_{s}^{a_s}\ \\
&=& \prod_{i=1}^{s} P_{i}^{a_i}\ \\
&where&\ P_1 < P_2 < ... < P_s \leq n\ ,\ \ P_i \ is\ PRIME\ ,\ \\
& &\ a_i \geq 1\ ,\ for\ all\ i\ \in [\ 1, s\ ]\ ,\ \ s \in\ [\ 1, n\ ] \cap Z^+\ . \\
\end{array}\)
Unique Factorization Theorem
https://brilliant.org/wiki/fundamental-theorem-of-arithmetic/
The fundamental theorem of arithmetic (FTA), also called the unique-prime-factorization theorem,
states that every integer greater than than 1:
- either is prime itself
- or is the product of a unique combination of prime numbers.
Music Hackathon: EMI Music Data Science Hackathon
https://www.kaggle.com/c/MusicHackathon
Music Data Science Hackathon Prizes (sponsored by EMI and EMC), - July 21st - 24 hours
- 1st Global Prize – £2,500
- 2nd Global Prize – £1,000
- 3rd Global Prize – £500
- London Venue Prize - £2,000
- Data Visualization Prize - £500 (sponsored by Adatis)
fastFM: A Library for Factorization Machines
https://jmlr.csail.mit.edu/papers/volume17/15-355/15-355.pdf
pyFM: Factorization Machines in Python
https://github.com/coreylynch/pyFM
polylearn: A library for factorization machines and polynomial networks
mainly for classification and regression in Python.
https://contrib.scikit-learn.org/polylearn/index.html
Maximum number of prime factors a number can have with exactly x factors
https://www.geeksforgeeks.org/maximum-number-of-prime-factors-a-number-can-have-with-exactly-x-factors/