| Author | Message | Time |
|---|---|---|
| Yoni | This question appeared in a national mathematics olympiad a few years ago. It was the easiest question on the test. I remember that when I participated, I couldn't solve this one. But now I was looking through old papers, I found this question again, thought about it for 3 minutes - and solved it. :) Here is the riddle in its original phrasing (translated to English). "For which natural numbers n will the numbers n+1, n+11, n+111 all be prime?" (Hint: The solution is quick and elegant.) For anyone who's interested but can't solve it right away, please go ahead and post your comments/thoughts anyway. :) | October 19, 2004, 5:35 AM |
| Mr. Neo | n=2 2+1=3, Prime. 2+11=13, Prime. 2+111=113, Prime. That's the only one that I could find, perhaps I am missing a few. | October 19, 2004, 11:43 AM |
| The-Rabid-Lord | could N= any even number? | October 19, 2004, 6:14 PM |
| UserLoser. | n=0 | October 19, 2004, 8:21 PM |
| Hitmen | [quote author=UserLoser link=topic=9231.msg85228#msg85228 date=1098217265] n=0 [/quote] 1 is not a prime number. | October 19, 2004, 8:41 PM |
| Mr. Neo | [quote author=Meh link=topic=9231.msg85210#msg85210 date=1098209690] could N= any even number? [/quote] No, take 6 for an example. 6+1 is 7, which is a prime number. 11+6 is 17, which is also a prime number, but 111+6=117 which is not a prime number. | October 19, 2004, 9:13 PM |
| K | [quote author=UserLoser link=topic=9231.msg85228#msg85228 date=1098217265] n=0 [/quote] 111 / 3 = 37. [quote author=Meh link=topic=9231.msg85210#msg85210 date=1098209690] could N= any even number? [/quote] 11 + 4 = 15. 15 / 3 = 5. | October 19, 2004, 9:24 PM |
| Adron | Quick answer, check the first line for big clue... [quote][black] n + 1, n + 2 + 3*3, n + 3*37 One of those will be divisible by three, so the only possibility is when that one is equal to three (since three itself is prime). [/black][/quote] | October 19, 2004, 9:27 PM |
| iago | Incidentally, Natural numbers are 1+, Whole numbers are 0+, and Integers are positive or negative with no decimal (I forget how it's defined). | October 20, 2004, 6:13 PM |
| TheMinistered | n=infinity | October 26, 2004, 2:42 AM |
| Yoni | [quote author=TheMinistered link=topic=9231.msg86149#msg86149 date=1098758553] n=infinity [/quote]Hmmmmmmmmmmmmm, no. (Adron's post is the answer, read it for a spoiler) | October 26, 2004, 7:57 AM |
| Slaughter | Yoni, I recently returned to the forums, sorry about this belated post - I understand the answer, but not how you came to the conclusion. | December 4, 2004, 6:52 PM |