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        riddles >> medium >> Diophantine inequality
        
(Message started by: JocK on May 27^th, 2006, 6:56am)

Title: Diophantine inequality
Post by JocK on May 27^th, 2006, 6:56am

Does a solution to |2^x - 3^y| < e^y-pi exist for integer x, y > 0?

Title: Re: Diophantine inequality
Post by Barukh on May 27^th, 2006, 9:21am

If I did my calculations right, [hide]one needs to check only values y < 52[/hide].

:-/

Title: Re: Diophantine inequality
Post by JocK on May 27^th, 2006, 11:19am

Ooops... made a stupid error... :-[

Will repost the problem (corrected and in a more generalised form). Sorry for messing up.

Title: Re: Diophantine inequality
Post by Eigenray on May 27^th, 2006, 12:37pm

on 05/27/06 at 09:21:08, Barukh wrote:

If I did my calculations right, [hide]one needs to check only values y < 52[/hide].

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???