Oooops, you are perfectly right. Not checked this result directly given by the computer, I was too happy to have seen something on the screen this morning... This problem on base 4 is a precision problem, 14 digits were too long for my program. Sorry. I have already deleted the result on the base 4 in http://cboyer.club.fr/FractionsDigits.htm Who can provide at least one solution in base 4? Christian. -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Mike Speciner Envoyé : mardi 26 septembre 2006 17:23 À : math-fun Objet : Re: [math-fun] Decimal question I don't see how the base 4 solutions you've posted can work. The denominators have prime factors other than 2 that are not in the numerators, so how can their quaternals (?) terminate? --ms Christian Boyer wrote:
Base 4 is not impossible, most compact solutions found. Completely incredible, they have 14 digits!!! So strange. If somebody can check, I hope to have not missed easiest solutions in base 4.
Including the crazy results on base 4, including the sudoku-like solution 124,983/576 = 216.984 375 all the main numerical results on this decimal question are now in this page:
http://cboyer.club.fr/FractionsDigits.htm
And an Excel file can be downloaded from this page, including the full list of solutions from 2 to 8 digits, starting by the solution 5/2 = 2.5 (using our classical base 10).
David, thanks for your interesting question.
Christian.
-----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Christian Boyer Envoyé : lundi 25 septembre 2006 21:57 À : 'math-fun' Objet : RE: [math-fun] Decimal question
You know that the most compact solution in base 10 is:
5/2 = 2.5
But in other bases? I have now the most compact solutions of all (non-prime) bases <= 16. For example, in base 6, the most compact solution is:
35/4 = 5.43 Hmmm... difficult to read with our "decimal eyes"... The same irreducible fraction written in base 10: 23/4 = 5.75
In fact, only ONE exception: in the small base 4, I have not yet found any solution. Is the problem impossible in base 4, for an unknown reason?????
Christian.
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