Some years ago I mentionned that conjecture, but didn’t really make any progress then. Recently, I’ve tried again and found what could be a simple proof, which I’ve put here.

There may still be a silly mistake somewhere, but at least that seems to be going in the right direction. Comments welcome…

UPDATE (9 june 2011): well, it was blatantly wrong indeed… The paper has now been retracted, with apologies for the waste of time.

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This entry was posted on June 9, 2011 at 6:45 am and is filed under arxiv, mathematics. You can follow any responses to this entry through the RSS 2.0 feed.
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June 9, 2011 at 1:55 pm |

I’m afraid that Corollary 2.2 in your paper is false.

Take for instance i = n = 5 and k = 4. The catch is that

the polynomials F_k have rational, but not necessarily integer

coefficients. Without Corollary 2.2 the proof of Theorem 2.3

collapses.

June 9, 2011 at 2:51 pm |

Dear Sir,

thank you for pointing it out: you are correct of course, I overlooked this unfortunately and have now retracted the paper.

I hope someone will solve this problem one day, it is quite captivating…