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構成的完全証明：Beal予想 / Constructive Proof of the Beal Conjecture\n\nこのリポジトリは、Beal予想に対する構成的完全証明を収録しています。\n\n## 🔍 問題概要\n\nBeal予想とは、次の形の等式に関する未解決問題です：\n\n\u003e \\( A^x + B^y = C^z \\quad\text{かつ}\\quad x, y, z \u003e 2 \\Rightarrow \\gcd(A, B, C) \u003e 1 \\)\n\nこれはフェルマーの最終定理の拡張とも言われ、共通因数の存在が必須であることを主張します。\n\n## ✅ 証明の特徴\n\n- A型素数と構成的指数密度モデルによる除外領域の構成\n- ABC予想モデルの拡張による指数和の稀薄性の証明\n- 共通因数なしの領域における零密度化と除去関数の使用\n- 構成的定義・補題・定理ブロックによる段階的な証明展開\n\n## 📂 ディレクトリ構成\n\n```\n.\n├── main.tex\n├── sections/\n│   ├── introduction.tex\n│   ├── exponential_structure.tex\n│   ├── gcd_filtering.tex\n│   ├── abc_extension.tex\n│   ├── theorem_proof.tex\n│   └── conclusion.tex\n├── README.md\n├── LICENSE\n├── compile.sh\n└── .gitignore\n```\n\n## 🧠 証明論的アプローチ\n\n- \\( A^x + B^y = C^z \\) の共通因数なし領域を構成的に除去\n- 既存のABC構成理論を指数項へ一般化\n- 排除領域が零密度となることを証明する除去関数を定義\n\n## 🌐 GitHub Topics（推奨）\n\n```\nmath\nnumber-theory\nbeal-conjecture\nconstructive-mathematics\nabc-extension\ngcd-analysis\nlatex\narxiv-compatible\n```\n\n## ✍️ ライセンス\n\n本リポジトリは [CC BY-NC 4.0](https://creativecommons.org/licenses/by-nc/4.0/) に従って公開されています。\n\n---\n_この証明は、AIと人間の協働による構成的数論の体系構築の一環として完成されました。_\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmk9207%2Fbeal-conjecture-constructive-proof","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmk9207%2Fbeal-conjecture-constructive-proof","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmk9207%2Fbeal-conjecture-constructive-proof/lists"}