Theorem (elementary divisibility properties)
Exercise
symbol. Restate the statement of the theorem in English (not just translate quantifiers, but make the statement make sense!). Rewrite the statement using the
Problem
Prove the theorem using the definitions of divisibility. Hint: actually provide the
from the definition!
Theorem (divisibility properties)
- If
and , then . - If
and , then . - If
and , then .
Problem (prep)
Prove the theorems above using the definition of divisibility.