Later, I found on the same website that I originally found the problem a proof showing there was a single unique solution.

Can you post the proof? I got as far as Mathsy did, that two of the numbers should be odd and one even. Maybe, the proof has got something to do with 2 being the only even prime

]]>... but the hide tag has a problem with apostrophes.

I think I got the hide tag straightened out. Quotes should work now

]]>I know I am new here but I'm quite impressed with the speed that you found an answer.

]]>I said it was easy.

]]>Below is a copy of the output file.

```
Bounded integer solutions list
Bounds: x:[1;500] y:[1;500] z:[1;500]
--------------------------
x y z
2 3 5
2 5 3
3 2 5
3 5 2
5 2 3
5 3 2
--------------------------
6 solutions found
```

And with more and more attempts I always get this result. 6 Solutions! Could it be?

I know that brute-forcing the equation WILL NEVER PROVE that *ONLY* 6 solutions exist...

Even if I asked the program to search within bounds [1 to 50000000000]...we don't know if 50000000001 has a solution...

Its not the maths way. But it can give us great clues!

Just for curiosity...even from 1 to 5000 there are still only these 6 solutions : )

Sorry to anyone uptight about punctuation, but the hide tag has a problem with apostrophes.

Anyway, if you read that, you can see that it was mostly guesswork that got it and we're still nowhere near proving that that's the only combination. I've got as far as showing that there needs to be 1 even and 2 odd, but beyond there I'm stuck.]]>

This is one of my favorite integer problems. The wording is a little off. I think it should read, "their product is evenly divisible", no fractions. I think there is also a proof that shows there is exactly one solution to this problem. When posting solutions, please post your method as well.

(x × y 1) ÷ z = (int)

(y × z 1) ÷ x = (int)

(z × x 1) ÷ y = (int)