本原勾股方程

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

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

Treenewbee

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

小一点的解：
\[151* \left(3^{4094548} 17^{8100} 10^{4096576}\right)^{2023}+157* \left(3^{4092525} 17^{8096} 10^{4094552}\right)^{2024}-149* \left(3^{4090504} 17^{8092} 10^{4092530}\right)^{2025}\]

蔡家雄

求：\(3*x^{131}+4*y^{137}+5*z^{139}=6*w^{149}\)

Treenewbee

蔡家雄 发表于 2024-3-18 18:42
求：\(3*x^{131}+4*y^{137}+5*z^{139}=6*w^{149}\)

\[3 \left(2^{2799321}\right)^{131}+4 \left(2^{2676723}\right)^{137}+5 \left(2^{2638209}\right)^{139}=6 \left(2^{2461148}\right)^{149} \]

Treenewbee

小一点：\[3 \left(2^{1145777}\right)^{131}+4 \left(2^{1095597}\right)^{137}+5 \left(2^{1079833}\right)^{139}=6 \left(2^{1007361}\right)^{149}\]

Treenewbee

再小一点\[3 \left(2^{667669}\right)^{131}+4 \left(2^{638428}\right)^{137}+5 \left(2^{629242}\right)^{139}=6 \left(2^{587011}\right)^{149}\]

Treenewbee

再小一点：\[3* \left(3^{63888}\right)^{131}+4 *\left(3^{61090}\right)^{137}+5 *\left(3^{60211}\right)^{139}=6*\left(3^{56170}\right)^{149}\]

蔡家雄

求：\(14*x^{87}+10*y^{91}=6*z^{95}\)

Treenewbee

蔡家雄 发表于 2024-3-19 10:00
求：\(14*x^{87}+10*y^{91}=6*z^{95}\)

\[14* \left(2^{8099}\right)^{87}+10* \left(2^{7743}\right)^{91}=6 *\left(2^{7417}\right)^{95}\]