The "Difficulties" in Fermat's Original Discourse on the Indecomposability of Powers Greater Than a Square: A Retrospect

This preprint reconstructs a possible version of the original proof of the indecomposability of powers greater than a square, as referenced by Pierre Fermat. Using methods accessible in Fermat’s era, it provides a systematic derivation and analysis, clarifying why integer solutions exist only for the cases n = 1 and n = 2. The work may interest researchers in number theory and the history of mathematics.