Prime factorization (PF)

[Savage]

I am not asking about how to do a PF but rather what a PF tells us about a number. Google was no help.

I do know you can use it to find the sum of a numbers divisors, find all the numbers divisors, do theta^2 (abstract algebra concept)...that is about it. Any other cool things I should know?

[Zawadx]

Well, PFs (or PPF, Prime Power Factorization) is at the core of Number Theory so I don't think it'll relate to many 'cool' stuff. However, PPF is used in the Proof of the Fundamental Theorem of Arithmetic, which is pretty nice.

[Pineapple]

Yup. To save you the time googling, the FTA says that every natural number is associated with a unique prime factorization. The converse of the relation is obviously true, as every prime factorization is only associated with 1 unique natural number - its product. However, the fact that there's no way to prime factorize the same number in two different ways is pretty cool, imho.

Just wondering, how familiar are you with competition-level math problem solving?

[Zawadx]

Just wondering, how familiar are you with competition-level math problem solving?

Dunno if this was aimed at me or Savage But yeah, I have participated in math olympiads for the last 4 years, once becoming the top in my country in my category and once becoming second ^^ This year I even went to the Team Selection Camp for the IMO. So I'm pretty familiar with competition level math including Number Theory, Combinatorics, Functions and Plane Euclidean Geometry.
 

[DoubleCapitals]

Just wondering, how familiar are you with competition-level math problem solving?

Dunno if this was aimed at me or Savage But yeah, I have participated in math olympiads for the last 4 years, once becoming the top in my country in my category and once becoming second ^^ This year I even went to the Team Selection Camp for the IMO. So I'm pretty familiar with competition level math including Number Theory, Combinatorics, Functions and Plane Euclidean Geometry.

Woah, that's nice! Teach me how you do it one day, would you?

[CuCN]

once becoming second

Who was in Antarctica to beat you?

[Zawadx]

Well only top-notch scientists live here, so I have to compete with their genius kids

[Savage]

Ok thanks guys