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共轭根式的常见问题

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hbghlyj posted 2020-1-29 22:52 |Read mode
Last edited by hbghlyj 2020-1-29 23:06求所有>1的整数对(m,n),使得存在整数a,b,x,y,a',b',
$\sqrt[m]{b},\sqrt[m]{b'}$是无理数,$(a + \sqrt[m]{b})^n = {\rm{x}} + \sqrt[m]{y},(a' - \sqrt[m]{b'})^n= {\rm{x}} - \sqrt[m]{y}$.

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original poster hbghlyj posted 2023-9-8 13:14
例如$m=n=2$
$a>0$
$(a+\sqrt b)^2=a^2+b+\sqrt{4a^2b}$
$(a-\sqrt b)^2=a^2+b-\sqrt{4a^2b}$

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