When I'm solving problems, I'm often confronted to solving equations, and when I'm solving equations, I'm often confronted to find the natural solutions of these equations.
My actual personal insolvable problem is : How to determine the natural solutions of an equation ? For example, let's take this rather simple equation :
$9 = a+b$
I want to solve it, knowing that $a$ and $b$ are natural numbers. How can I get all the possible answers ? Am I obliged to test every possible value for $a$ and $b$ ? I need Mathematics wisdom.