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フェルマーの最終定理ならこれでどうぞ
**Critical review of “Another proof of Fermat’s Last Theorem” (Kouji Takaki)**
This manuscript does not provide a valid proof of Fermat’s Last Theorem because several key reductions and auxiliary constructions are logically unjustified. The issues below are “fatal” in the sense that the argument cannot proceed without repairing them.

**(1) Invalid “without loss of generality” reduction on common prime factors.**

The text effectively assumes that the variables (x,y,z) do not share prime factors in a way stronger than the standard primitive reduction. In a correct FLT setup one may assume (gcd(x,y,z)=1) by dividing out a common factor. However, the manuscript treats stronger pairwise coprimality-style conditions (or “no two share a prime factor”) as if they followed without loss of generality. This is not legitimate: from (gcd(x,y,z)=1) it does **not** follow that (gcd(x,z)=1) or (gcd(y,z)=1). Any subsequent reasoning that depends on these stronger coprimality assumptions fails to be logically sound.