Giuga-Agoh redux

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UPDATE (9 june 2011): well, it was blatantly wrong indeed…  The paper has now been retracted, with apologies for the waste of time.

 

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2 Responses to “Giuga-Agoh redux”

  1. Robin Chapman Says:

    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.

    • Thomas Sauvaget Says:

      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…

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