Find all triples (x,y,z) for this equation where x, y, and z are natural numbers
I figured out all the triples just through trial but I don't understand how you're supposed to figure it out. Can someone help me?
The best way I see to do this is by restricting the possible cases. Say that . Then we can see that and . This gives us the some cases to try . And any permutation will be a solution of that.
I sort of understand that but could you explain why and ?
Because otherwise it would be impossible to get 2008. Note, is the smallest this means but if then would exceede 2008. Similarly with . The last constraint comes from because if then would already exceede 2008.