本原勾股方程

蔡家雄

求：\(6*x^{41}+8*y^{43}=z^{47}\)

蔡家雄

求：\(x^{71}+y^{73}=34*z^{79}\)

Treenewbee

蔡家雄 发表于 2024-3-18 09:42
求：\(x^{6}+y^{10}=2*z^{14}\)

\[\left(2^{35 k}\right)^6+\left(2^{21 k}\right)^{10}=2 \left(2^{15 k}\right)^{14}\]

Treenewbee

蔡家雄 发表于 2024-3-18 09:52
求：\(6*x^{41}+8*y^{43}=z^{47}\)

\[6 \left(2^{1246} 3^{431}\right)^{41}+8 \left(2^{1188} 3^{411}\right)^{43}=\left(2^{1087} 3^{376}\right)^{47}\]

Treenewbee

蔡家雄 发表于 2024-3-18 09:52
求：\(6*x^{41}+8*y^{43}=z^{47}\)

两个稍大一点的解：\[6 \left(2^{666} 3^{1097}\right)^{41}+8 \left(2^{635} 3^{1046}\right)^{43}=\left(2^{581} 3^{957}\right)^{47}\]
\[6 \left(2^{1183} 3^{1011}\right)^{41}+8 \left(2^{1128} 3^{964}\right)^{43}=\left(2^{1032} 3^{882}\right)^{47}\]

Treenewbee

蔡家雄 发表于 2024-3-18 09:56
求：\(x^{71}+y^{73}=34*z^{79}\)

\[\left(2^{148}\right)^{71}+\left(2^{144}\right)^{73}=34 *\left(2^{133}\right)^{79}\]

蔡家雄

求：\(30*x^{71}+16*y^{73}=34*z^{79}\)

Treenewbee

蔡家雄 发表于 2024-3-18 10:28
求：\(30*x^{71}+16*y^{73}=34*z^{79}\)

\[30 *\left(2^{2044} 30^{3249}\right)^{71}+16 *\left(2^{1988} 30^{3160}\right)^{73}=34* \left(2^{1837} 30^{2920}\right)^{79}\]

蔡家雄

求：\(151*x^{2023}+157*y^{2024}=149*z^{2025}\)

Treenewbee

蔡家雄 发表于 2024-3-18 12:33
求：\(151*x^{2023}+157*y^{2024}=149*z^{2025}\)

\[151 \left(2^{4092522} 3^{12150} 833^{2048288}\right)^{2023}+157 \left(2^{4090500} 3^{12144} 833^{2047276}\right)^{2024}=149 \left(2^{4088480} 3^{12138} 833^{2046265}\right)^{2025}\]