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Topic: Diophantine inequality (Read 408 times) |
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JocK
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Diophantine inequality
« on: May 27th, 2006, 6:56am » |
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Does a solution to |2x - 3y| < ey-pi exist for integer x, y > 0?
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| « Last Edit: May 27th, 2006, 7:13am by JocK » |
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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.
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Barukh
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Re: Diophantine inequality
« Reply #1 on: May 27th, 2006, 9:21am » |
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If I did my calculations right, one needs to check only values y < 52.
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JocK
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Re: Diophantine inequality
« Reply #2 on: May 27th, 2006, 11:19am » |
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Ooops... made a stupid error... 
Will repost the problem (corrected and in a more generalised form). Sorry for messing up.
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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.
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Eigenray
wu::riddles Moderator
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Re: Diophantine inequality
« Reply #3 on: May 27th, 2006, 12:37pm » |
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on May 27th, 2006, 9:21am, Barukh wrote:| If I did my calculations right, one needs to check only values y < 52. |
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That's a lot better than y < (232/(1-1/log 3))49 ~ 10523, which is (I think) what I get from the abstract for Ellison's paper:
Ellison, W. J. On a theorem of S. Sivasankaranarayana Pillai. Séminaire de Théorie des Nombres, 1970--1971 (Univ. Bordeaux I, Talence), Exp. No. 12, 10 pp. Lab. Théorie des Nombres, Centre Nat. Recherche Sci., Talence, 1971.
According to Goettinger Digitalisierungszentrum, volume 1 of the Seminaire de Théorie des Nombres de Bordeaux is 1971-1972. Is there a volume 0
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