Discussion in 'Math Research' started by Hugo Pfoertner, Jul 2, 2003.

  1. Some weeks ago Alex Liu posted the following question to NG
    sci.math.research: Title was: "Diophantine equation with factorial"

    There was no reaction to this question. I wrote a little program to
    understand, why there are no other solutions:
    which produced the results:

    x^3+y^3 can be written as (x+y)*(x^2-x*y+y^2)

    (x^2-x*y+y^2) can only produce factors 3, square factors or factors
    of the form 6*k+1. The missing factors needed to produce n!
    must all come from (x+y) which
    doesn't grow fast enough to keep track with the highest factors
    of the form 6*k+1 produced by (x^2-x*y+y^2).

    Looking for a more rigorous treatment...


    Hugo Pfoertner
    Hugo Pfoertner, Jul 2, 2003
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