Testing UI

Author: karevvv

_posts/2025-02-12-Number_Theory_-_Part_1.md

@@ -17,14 +17,19 @@ description: This is an introductory course to number theory and its application
 Hey there, welcome to this post. This post is inspired by my math discrete math/number theory class in university. I am by no means a math/number theory expert and this course is just an intro to it. This series is meant to help those who don't have any basics in number theory to gain some foundational knowledge. If you want to know more, feel free to google or ask an expert. This course will be split into 3-4 parts and this part is all about modulo. Lets start!
 
 ### Division theorem
->let a be a whole number and d be a positive whole number, then there exists a unique whole number q and r with $0\leq r<d$ such that $a=dq+r$
+>let `a` be a whole number and `d` be a positive whole number, then there exists a unique whole number `q` and `r` with $0\leq r<d$ such that $a=dq+r$
 {: .prompt-info}
 
 Lets see an example:
+
 `a` = 10
+
 `d` = 3
+
 find q, and r
+
 We can easily see that $10 = 3\times3 +1$ , so q is 3 and r is 1
+
 >Remember that $0\leq r<d$ meaning that, for the above example, `q` = 2, `r` = 4 or `q` = 4, `r` = -2, although does make 10, is not a valid answer
 {: .prompt-warning}
 
@@ -45,5 +50,13 @@ For a pair of `a` and `d` where the remainder is 0, such as practice
 no. 3, we can say that `d` divides `a`, or in math notations, $d|a$. In 
 other words, $d|a$ means that $a=d\times q$.
 
+### Divisibility
+if $d|a$ , then `d` is a factor of `a` and `a` is a multiple of `d` 
+
+
+Here are some theorems for divisibility:
 
+- if a|b and a|c then a|(b+c)
+- if a|b then a|bc for all integer c
+- if a|b and b|c then a|c