四十年，才准确定位。

lusishun

朱明君 发表于 2024-1-20 13:50
\(x^5+y^2=z^2\)
\(解：原方程是3^1-1^1=2^1\)
\(则\left( 3^3\right)^5+\left( 1\times3^7\right)^2=\le ...

与朱老师交流一题：
X^41+y^20=z^20

lusishun

x^50+y^50=z^101

朱明君

lusishun 发表于 2024-1-20 21:11
x^50+y^50=z^101

\(\left( 2^2\right)^{50}+\left( 2^2\right)^{50}=2^{101}\)

朱明君

lusishun 发表于 2024-1-20 21:09
与朱老师交流一题：
X^41+y^20=z^20

\(\left( 2^{40}-1\right)^{41}+\left( \left( 2^{40}-1\right)^2\right)^{20}=\left( \left( 2\times\left( 2^{40}-1\right)\right)^2\right)^{20}\)

lusishun

朱明君 发表于 2024-1-21 08:09
\(x^7+y^{21}=z^{20}\)

X=2^57,
Y=2^19,
z=2^20

lusishun

X^32+y^97=z^32


X^24+y^97=z^24.

朱明君

\(设n为正整数，且n=ab，\)
\(则x^n+y^{n+1}=z^n\)
\(则x^{ab}+y^{ab+1}=z^{ab}\)
\(则\left( 2^n-1\right)^n+\left( 2^n-1\right)^{n+1}=\left( 2\times\left( 2^n-1\right)\right)^n\)
\(则\left( 2^{ab}-1\right)^{ab}+\left( 2^{ab}-1\right)^{ab+1}=\left( 2\times\left( 2^{ab}-1\right)\right)^{ab}\)
\(则\left( \left( 2^n-1\right)^b\right)^a+\left( 2^n-1\right)^{n+1}=\left( \left( 2\times\left( 2^n-1\right)\right)^b\right)^{a}\)
\(则\left( \left( 2^n-1\right)^a\right)^b+\left( 2^n-1\right)^{n+1}=\left( \left( 2\times\left( 2^n-1\right)\right)^a\right)^b\)
\(则\left( \left( 2^n-1\right)^b\right)^a+\left( 2^n-1\right)^{n+1}=\left( \left( 2\times\left( 2^n-1\right)\right)^a\right)^b\)
\(则\left( \left( 2^n-1\right)^a\right)^b+\left( 2^n-1\right)^{n+1}=\left( \left( 2\times\left( 2^n-1\right)\right)^b\right)^a\)

\(设n为正整数，且n=ab，\)
\(则x^n+y^n=z^{n+1}\)
\(则x^{ab}+y^{ab}=z^{ab+1}\)
\(则2^n+2^n=2^{n+1}\)
\(则2^{ab}+2^{ab}=2^{ab+1}\)
\(则\left( 2^b\right)^a+\left( 2^b\right)^a=2^{n+1 }\)
\(则\left( 2^a\right)^b+\left( 2^a\right)^b=2^{n+1}\)
\(则\left( 2^a\right)^b+\left( 2^b\right)^a=2^{n+1}\)

lusishun

X^12+y^97=z^12,

X^6+y^97=z^6

朱明君

n=ab，n=96
96=1×96=2×48=3×32=4×24=6×16=8×12

朱明君

\(x^{13}+y^{19}=z^2\)