Susil Kumar Jena - On xn + yn = n!zn

cm:9473 - Communications in Mathematics, June 29, 2018, Volume 26 (2018), Issue 1 - https://doi.org/10.2478/cm-2018-0002
On xn + yn = n!znArticle

Authors: Susil Kumar Jena

    In p. 219 of R.K. Guy's Unsolved Problems in Number Theory, 3rd edn., Springer, New York, 2004, we are asked to prove that the Diophantine equation xn + yn = n!zn has no integer solutions with n ∈ N+ and n > 2. But, contrary to this expectation, we show that for n = 3, this equation has in finitely many primitive integer solutions, i.e. the solutions satisfying the condition gcd(x, y, z) = 1.


    Volume: Volume 26 (2018), Issue 1
    Published on: June 29, 2018
    Imported on: May 11, 2022
    Keywords: [MATH]Mathematics [math]

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