>>301

As a correction(>>300), I already stated that my ((6,10,15)) example was not intended as a counterexample under the additional condition “(x^n+y^n=z^n).”

Now, on your current claims:

You wrote: “自明な内容に補題の引用は必要ない。”

I am not asking for an external citation. I am asking you to state the *explicit inference* you rely on, so the step can be checked.

You wrote: “z^n=abであり、aとbが互いに素であるからbがn乗数だと書いているだけ。”

From (z^n=ab) and (gcd(a,b)=1), the valid conclusion is that **both** (a) and (b) are (n)-th powers. This is not automatic “by wording”; it requires the standard prime-exponent argument (unique factorization): since (ab) is an (n)-th power and (a,b) share no prime factors, the exponent of each prime in (a) (and in (b)) must be a multiple of (n).

So please state clearly: (i) where you establish (gcd(a,b)=1), and (ii) whether you are using this prime-exponent argument (or an equivalent lemma). Without (i) and (ii), the step “(b) is an (n)-th power” is not justified.

You also wrote: “If z≢0 (mod a) holds, then x^n+y^n≡0 (mod n) holds …”

As written, the modulus changes from “mod (a)” to “mod (n)” with no justification. Please point to the exact line in your paper and write the congruence with the correct modulus before claiming a contradiction.