Propostion 2.3.9 (Euclidean algorithm). Let \(n\) be a natural number, and let \(q\) be a positive number. Then there exist natrual numbers \(m,r\) such that \(0\leq r<q\) and \(n=mq+r\).
\(Proof\). See Exercise 2.3.5.
Proposition 2.3.9
-
Exercise 2.3.5 (Proposition 2.3.9)
2.3.5 Prove Proposition proposition 2.3.9 (Hint: fix \(q\) and induct on \(n\).)
-
Chapter2
Exercise 2.3.5. Prove Proposition proposition 2.3.9