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wu :: forums    riddles    medium (Moderators: Icarus, Eigenray, SMQ, Grimbal, towr, william wu, ThudnBlunder)    Difference of powers « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Difference of powers  (Read 443 times) NickH Senior Riddler     Gender: Posts: 341 Difference of powers   « on: May 1st, 2003, 3:18pm » Quote Modify Find all ordered pairs (m,n) of positive integers such that |3m - 2n| < 10. IP Logged Nick's Mathematical Puzzles Leo Broukhis Senior Riddler     Gender: Posts: 459 Re: Difference of powers   « Reply #1 on: Jul 8th, 2003, 9:14am » Quote Modify (1,2) (2,1) (2,2) (1,3) (2,3) (2,4) (3,5)   What did I miss? IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Difference of powers   « Reply #2 on: Jul 8th, 2003, 9:55am » Quote Modify on Jul 8th, 2003, 9:14am, Leonid Broukhis wrote: What did I miss? (1,1) IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Leo Broukhis Senior Riddler     Gender: Posts: 459 Re: Difference of powers   « Reply #3 on: Jul 8th, 2003, 10:30am » Quote Modify That was a stupid mistake: I started listing pairs from (0,0), then realised that m and n must be positive, and cut a group of lines that contained 0. (1,1) must have been somewhere among them. But really, why is it medium? Because of (3,5)? Or because you need to prove that there are no more? Well, continuous fractions of log(3)/log(2) help to do that. « Last Edit: Jul 8th, 2003, 10:31am by Leo Broukhis » IP Logged NickH Senior Riddler     Gender: Posts: 341 Re: Difference of powers   « Reply #4 on: Jul 9th, 2003, 12:45pm » Quote Modify I placed it in medium because of the need to prove there are no more.   Please could you expand on the continued (?) fractions technique? IP Logged Nick's Mathematical Puzzles Leo Broukhis Senior Riddler     Gender: Posts: 459 Re: Difference of powers   « Reply #5 on: Jul 9th, 2003, 5:21pm » Quote Modify After some thought, maybe it doesn't help to prove that there are no more, only to make me convinced about it. IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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