用公式法求解特殊佩尔方程

Treenewbee

\[2^2+3^1+3^2=2^4\]

\[(2^{521285}*3^{312246})^{131} + (2^{498455}*3^{298571})^{137} +
(2^{491283}*3^{294275})^{139} = (2^{458311}*3^{274525})^{149}\]

Treenewbee

\[2^0 + 2^2 + 3^3 = 2^5\]

\[(2^{483199}*3^{108298})^{131} + (2^{462037}*3^{103555})^{137} + (2^{455389}*3^{102065})^{139} = (2^{424826}*3^{95215})^{149}\]

lusishun

Treenewbee 发表于 2024-2-21 01:25
\[2^0 + 2^2 + 3^3 = 2^5\]

\[(2^{483199}*3^{108298})^{131} + (2^{462037}*3^{103555})^{137} + (2^{4 ...

(3^2799321)^131+(3^267623)^137+(3^2638209)^139=(3^2961148)^149

蔡家雄

求：\(x^3+y^5+z^7+r^{11}+t^{13}+u^{17}+v^{19}=w^{23}\)

用：\(2^0+2^0+2^0+2^0+2^0+2^0+2^1=2^3\)

用：\(3^0+3^0+3^0+3^0+3^0+3^0+3^1=3^2\)

用：\(7^0+7^0+7^0+7^0+7^0+7^0+7^0=7^1\)

蔡家雄

求：\(x^3+y^5+z^7+r^{11}+t^{13}+u^{17}+v^{19}=w^{23}\)

解：\((7^{9699690})^3+(7^{5819814})^5+(7^{4157010})^7+(7^{2645370})^{11}+(7^{2238390})^{13}\)

\[+(7^{1711710})^{17}+(7^{1531530})^{19}=(7^{1265177})^{23}\]

Treenewbee

\[\left(2^{695205}\right)^{19}+\left(2^{776994}\right)^{17}+\left(2^{1016069}\right)^{13}+\left(2^{1200809}\right)^{11}+\left(2^{1886985}\right)^7+\left(2^{2641779}\right)^5+\left(2^{4402965}\right)^3=\left(2^{574300}\right)^{23}\]

wlc1

求：\(x^{16}+y^{30}+z^{34}=w^{38}\)

wlc1

求：\(x^{32}+y^{126}+z^{130}=w^{134}\)

cz1

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Treenewbee

\[\left(2^{684} 3^{4080}\right)^{16}+\left(2^{365} 3^{2176}\right)^{30}+\left(2^{322} 3^{1920}\right)^{34}=\left(2^{288} 3^{1718}\right)^{38}\]