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wu :: forums    riddles    easy (Moderators: SMQ, william wu, Grimbal, ThudnBlunder, Eigenray, Icarus, towr)    Splitting 2005 « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Splitting 2005  (Read 450 times) JocK Uberpuzzler     Gender: Posts: 877 Splitting 2005   « on: Jan 4th, 2005, 12:21pm » Quote Modify Can you write 2005 as the sum of:   a prime squared, a prime cubed and a prime to the fourth power? IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 Re: Splitting 2005   « Reply #1 on: Jan 4th, 2005, 1:15pm » Quote Modify Yes...   :: 20051/4~=6.69, so the largest prime 4th power we can use is 54: 2005-54=1380. 13801/3~=11.13, and as 11 is prime: 1380-113=49, which happens to be square.   Therefore, 2005=72+113+54 :: IP Logged mathschallenge.net / projecteuler.net Trebla Guest Re: Splitting 2005   « Reply #2 on: Jan 4th, 2005, 1:16pm » Quote Modify Remove One such answer, though I'd wager there are more... <<< 72+113+54=2005 >>> IP Logged Trebla Guest Re: Splitting 2005   « Reply #3 on: Jan 4th, 2005, 1:17pm » Quote Modify Remove Bah, I'm too slow... IP Logged JocK Uberpuzzler     Gender: Posts: 877 Re: Splitting 2005   « Reply #4 on: Jan 4th, 2005, 1:29pm » Quote Modify on Jan 4th, 2005, 1:17pm, Trebla wrote: Bah, I'm too slow... Well... grab your chance: no one has posted alternative solutions (yet)...!   IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Splitting 2005   « Reply #5 on: Jan 4th, 2005, 1:49pm » Quote Modify What alternatives are there? Or would you allow subtraction as well as addition in a sum? Or Gaussian primes? IP Logged Wikipedia, Google, Mathworld, Integer sequence DB JocK Uberpuzzler     Gender: Posts: 877 Re: Splitting 2005   « Reply #6 on: Jan 4th, 2005, 2:35pm » Quote Modify No gaussian primes please... I have taken Trebla's wager and won't allow cheating...   IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 Re: Splitting 2005   « Reply #7 on: Jan 4th, 2005, 4:09pm » Quote Modify If you're working in base 10 then there is only one solution.   However, if 2005 is not necessarily given in base 10, then there certainly exists solutions in base 12 and base 16. 200512 = 3461 = 532+33+54 200516 = 8197 = 792+113+54   But you did say...   on Jan 4th, 2005, 2:35pm, JocK wrote: I ... won't allow cheating IP Logged mathschallenge.net / projecteuler.net 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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