費(fèi)馬大定理推廣的一個(gè)特殊形式

2023-03-13 00:09 作者:我恨PDN定理 0人讀過 | 我要投稿

我們熟知的費(fèi)馬大定理，或稱為費(fèi)馬最后定理，是指以下的丟番圖方程無解： $x%5En%20%2By%5En%3Dz%5En%20%5C%20(n%3E2%20%5C%3A%E4%B8%94%5C%20xyz%5Cneq0%20)$

我們對(duì)這個(gè)式子進(jìn)行一步推廣，得到：

$a(x)%2Cb(x)%2Cc(x)%5Cin%20%5Cmathbb%7BC%7D%5C%2C%E4%B8%94%5C%2C%E4%B8%A4%5C%2C%E4%B8%A4%5C%2C%E4%BA%92%5C%2C%E7%B4%A0%0A%5C%5Ca%5En%2Bb%5En%5Cneq%20c%5En%20%5C%20(n%3E2)$

容易看出，當(dāng)三個(gè)多項(xiàng)式均為常數(shù)時(shí)，記為費(fèi)馬大定理的最初形式，我們這里假設(shè)三個(gè)多項(xiàng)式不為常數(shù)多項(xiàng)式. $%5Cbegin%7Balign*%7D%5Clabel%7B2%7D%0A%0A%26%20%5Cquad%20%E6%88%91%20%5C%2C%20%E4%BB%AC%20%5C%2C%20%E5%85%88%20%5C%2C%20%E7%BB%99%20%5C%2C%20%E5%87%BA%20%5C%2C%20%E9%9C%80%20%5C%2C%20%E8%A6%81%20%5C%2C%20%E7%9A%84%20%5C%2C%20%E5%BC%95%20%5C%2C%20%E7%90%86%20%5C%2C%20%E5%92%8C%20%5C%2C%20%E5%AE%9A%20%5C%2C%20%E7%90%86%20%5C%2C%20%2C%20%E8%AE%B0%20%5C%3B%20%20%20n_%7B0%7D(f(x))%20%20%20%5C%2C%20%E8%A1%A8%20%5C%2C%20%E7%A4%BA%20%5C%2C%20%20%20f(x)%20%5C%2C%20%20%20%E7%9A%84%20%5C%2C%20%E4%B8%8D%20%5C%2C%20%E5%90%8C%20%5C%2C%20%E5%A4%8D%20%5C%2C%20%E6%A0%B9%20%5C%2C%20%E4%B8%AA%20%5C%2C%20%E6%95%B0.%20%5C%5C%0A%26%20%E5%BC%95%20%5C%2C%20%E7%90%86%20%5Cquad%20%20%E8%8B%A5%20%5C%2C%20%20%20f(x)%2C%20g(x)%20%5Cin%20%5Cmathbb%7BC%7D%5Bx%5D%20%5Cbackslash%20%5Cmathbb%7BC%7D%20%2C%20%20%5C%2C%20%E5%88%99%5C%5C%0A%26%20%5Cquad%20(a)%3A%20%20%5Coperatorname%7Bdeg%7D%20f(x)%3D%5Coperatorname%7Bdeg%7D%5Cleft(f(x)%2C%20f%5E%7B%5Cprime%7D(x)%5Cright)%2Bn_%7B0%7D(f(x))%20%5C%5C%0A%26%20%5Cquad%20(b)%3A%20%20n_%7B0%7D(f(x)%20g(x))%20%5Cleq%20n_%7B0%7D(f(x))%2Bn_%7B0%7D(f(x))%20%2C%20%20%5C%2C%20%E7%AD%89%20%5C%2C%20%E5%8F%B7%20%5C%2C%20%E6%88%90%20%5C%2C%20%E7%AB%8B%20%5C%2C%20%E5%BD%93%20%5C%2C%20%20%20(f(x)%2C%20g(x))%3D1%20.%5C%5C%0A%26%E5%AE%9A%20%5C%2C%20%E7%90%86%20%5C%2C%20%20(Mason-Stothers)%20%5C%2C%20%20%E8%AE%BE%20%5C%2C%20%20%20f_%7B1%7D(x)%2C%20f_%7B2%7D(x)%2C%20f_%7B3%7D(x)%20%5Cin%20%5Cmathbb%7BC%7D%5Bx%5D%20%5Cbackslash%20%5Cmathbb%7BC%7D%20%2C%20%20%5C%2C%20%E8%8B%A5%20%5C%2C%20%20%20f_%7B1%7D(x)%2C%20f_%7B2%7D(x)%2C%20f_%7B3%7D(x)%20%20%5C%2C%20%20%E4%B8%A4%20%5C%2C%20%E4%B8%A4%20%5C%2C%20%E4%BA%92%20%5C%2C%20%E7%B4%A0%20%5C%2C%20%2C%20%20%5C%2C%20%E4%B8%94%5C%5C%0A%0A%26%20%5Cqquad%20f_%7B1%7D(x)%2Bf_%7B2%7D(x)%3Df_%7B3%7D(x)%5C%5C%0A%26%20%E5%88%99%5C%5C%0A%0A%26%20%5Cqquad%20%5Cmax%20%5Cleft%5C%7Bf_%7B1%7D(x)%2C%20f_%7B2%7D(x)%2C%20f_%7B3%7D(x)%5Cright%5C%7D%20%5Cleq%20n_%7B0%7D%5Cleft(f_%7B1%7D(x)%20f_%7B2%7D(x)%20f_%7B3%7D(x)%5Cright)-1%0A%5Cend%7Balign*%7D$

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標(biāo)簽：

五月天青色头像情侣网名,国产亚洲av片在线观看18女人,黑人巨茎大战俄罗斯美女,扒下她的小内裤打屁股

費(fèi)馬大定理推廣的一個(gè)特殊形式

費(fèi)馬大定理推廣的一個(gè)特殊形式的評(píng)論 (共條)

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費(fèi)馬大定理推廣的一個(gè)特殊形式

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