x^3+y^3=n!

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:
    http://www.randomwalk.de/scimath/x3py3.for
    which produced the results:
    http://www.randomwalk.de/scimath/x3py3.txt

    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...

    Thanks

    Hugo Pfoertner
     
    Hugo Pfoertner, Jul 2, 2003
    #1
    1. Advertisements

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.
Similar Threads
There are no similar threads yet.
Loading...