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wu :: forums    riddles    medium (Moderators: towr, william wu, SMQ, Grimbal, Eigenray, Icarus, ThudnBlunder)    quadruple « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: quadruple  (Read 2299 times) Christine Full Member     Posts: 159 quadruple   « on: Sep 15th, 2013, 4:56pm » Quote Modify Diophantus quadruple (1/16, 33/16, 17/4, 105/16)   the product of any two distinct terms + 1 is a square   How can you find other sets of rational quadruple? IP Logged SEMfuze Newbie     Posts: 11 Re: quadruple   « Reply #1 on: Sep 27th, 2013, 7:20am » Quote Modify y 2 = (a1x + n)(a2x + n)(a3x + n)(a4x + n)(a5x + n) IP Logged Christine Full Member     Posts: 159 Re: quadruple   « Reply #2 on: Sep 27th, 2013, 9:40am » Quote Modify on Sep 27th, 2013, 7:20am, SEMfuze wrote: y 2 = (a1x + n)(a2x + n)(a3x + n)(a4x + n)(a5x + n)   It doesn't look right. Maybe I miss something here. Please clarify. IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: quadruple   « Reply #3 on: Sep 27th, 2013, 2:35pm » Quote Modify I think he meant to copy/paste the formula for a hyperelliptic curve y2 = (a1x + 1)(a2x + 1)(a3x + n)(a4x + 1)(a5x + 1)  (n=1 in this case). Equation 2 on page 2 of http://arxiv.org/pdf/math/0002088.pdf, for example (I haven't read it, and not sure how much I'd understand of it if I would). IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Christine Full Member     Posts: 159 Re: quadruple   « Reply #4 on: Sep 27th, 2013, 5:15pm » Quote Modify on Sep 27th, 2013, 2:35pm, towr wrote: I think he meant to copy/paste the formula for a hyperelliptic curve y2 = (a1x + 1)(a2x + 1)(a3x + n)(a4x + 1)(a5x + 1)  (n=1 in this case). Equation 2 on page 2 of http://arxiv.org/pdf/math/0002088.pdf, for example (I haven't read it, and not sure how much I'd understand of it if I would).   Ouch! Thanks. The stuff on arxiv  is tough to understand. The question I posted is more difficult than I anticipated.     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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