SciTech-Mathmatics-UNIQUE FACTORIZATION THEOREM

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:
\(\large \begin{array}{ccl} n &=& P_{1}^{a_1} \cdot P_{1}^{a_1} \cdot ... \cdot P_{s}^{a_s}\ \\ &=& \prod_{i=1}^{s} P_{i}^{a_i}\ \\ &where& \ some\ s \geq 1\\, \\ & &\ P_1 < P_2 < ... < P_s \leq n\ ,\ and\ \ P_i \ is\ PRIME\ for\ all\ i,\ \\ & &\ a_i \geq 1\ ,\ for\ all\ i. \\ \end{array}\)