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You are not logged in. #1 20050803 01:03:43
Easy problemFind three positive whole numbers such that for any two of them, the number one less than their product is divisible by the third number. #2 20050803 01:40:27
Re: Easy problemDoes 1, 1 and 1 count? Why did the vector cross the road? It wanted to be normal. #3 20050803 01:59:58
Re: Easy problemAhh, good question. For this solution, x ≠y ≠z. For all values of x, y, z such that they are all integers, positive, and unique. #4 20050803 04:10:48
Re: Easy problemHere's my reasoning, hidden for anyone who wants to do it themselves: 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. Last edited by mathsyperson (20050803 04:12:21) Why did the vector cross the road? It wanted to be normal. #5 20050803 05:53:42
Re: Easy problemI coded a small program that searches for solutions. Code: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? #6 20050803 05:58:47
Re: Easy problemmathsyperson got it. He used the same method that I did, "plugandchug". Sometimes that's the best way to solve a problem. I also wrote a program to cycle all combinations of all integers from 1100,000 and only found one unique solution. Later, I found on the same website that I originally found the problem a proof showing there was a single unique solution. #7 20050803 06:01:53
Re: Easy problemkylekatarn is also correct. Technically, there are six solutions but they are all permutations of the same three numbers. #8 20050803 16:09:14
Re: Easy problem
I think I got the hide tag straightened out. Quotes should work now "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #9 20050803 17:11:24
Re: Easy problem
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 Character is who you are when no one is looking. 