1) Question: find x,y,z natural numbers such that the following is true:
$$ \frac{x}{y+z} + \frac{y}{x+z} + \frac{z}{x+y} = 4. $$
I was first presented the problem a more fun way:
(NOTE- a commenter pointed out that “Natural Numbers” and `Positive Whole Values’ are different since some people (and I AM one of them) include 0 as a natural. SO- to clarify, I want x and y and z to be naturals that are \(\ge 1\). )
2) Meta Question: When a blogger poses a question like that should they also post the answer? Have a pointer to the answer? Not have an answer? Pros and Cons:
a) If you do not list the answer at all (or post it in a few days) then people will not be tempted to look at the answer. They have to really work on it. (Maybe they can find the answer on the web).
b) There are people whose curiosity far exceeds their ego. So they want to work on in for (say) 5 minutes and then LOOK AT THE ANSWER! I am one of those people.
c) When you first look at a problem and work on it you are curious. If you have to wait a few days to get the answer then you may lose interest.
I invite you to work on both the question and the meta question. I will not be blocking people who post the answer in the comments, so if you want to work on it you might not want to look at the answers.
I will post the answer in a few days.