RE: The Mathematical Proof Thread
September 17, 2016 at 2:47 am
(This post was last modified: September 17, 2016 at 6:54 am by Alex K.)
Hello, everyone. Thanks for all of the beautiful posts. I am posting a proposition and my attempted proof of it (it is far from beautiful). I'd appreciate any tips or incites. Please do not assume this proof is correct until others have had a chance to pick it apart. This was exercise 36 (page 130) in Hammack's Book of Proof. Hammack only gives solutions for the odd exercises, so I'm not sure if this proof is valid. Also, I was not sure how to use a hide tag, so I apologize for posting the proof out in the open.
Relevant definitions:
Definition of Divisibility: Suppose a and b are integers. We say that a divides b if b=ac for some integer c. In this case we also say that a is a divisor of b, and that b is a multiple of a (Hammack, Book of Proof, pg 90).
Definition of the Least Common Multiple (LCM): The lcm of non-zero integers a and b, denoted lcm(a,b), is the smallest positive integer that is a multiple of both a and b (Hammack, Book of Proof, pg 90).
Proposition: Suppose a and b are natural numbers. Then a=lcm(a,b) if and only if b divides a
Proof Mini Strategy.
Relevant definitions:
Definition of Divisibility: Suppose a and b are integers. We say that a divides b if b=ac for some integer c. In this case we also say that a is a divisor of b, and that b is a multiple of a (Hammack, Book of Proof, pg 90).
Definition of the Least Common Multiple (LCM): The lcm of non-zero integers a and b, denoted lcm(a,b), is the smallest positive integer that is a multiple of both a and b (Hammack, Book of Proof, pg 90).
Proposition: Suppose a and b are natural numbers. Then a=lcm(a,b) if and only if b divides a
Proof Mini Strategy.
Moderator Notice
added hide tags
In source code mode:
-AK
added hide tags
In source code mode:
Code:
[hide]
secret
[/hide]
-AK