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[数论] 求最大公因数

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isee posted 2014-9-4 08:15 |Read mode

集合$\{16^n+10n-1|n\in Z^*\}$的最大公因数是什么？

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realnumber posted 2014-9-4 08:57

n=1,是25
$(15+1)^n+10n-1=25k+15n+1+10n-1=25k+25n$,k是某整数，二项展开。
所以答案是25.

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original poster isee posted 2014-9-4 08:59

回复 2# realnumber

被秒了。。。

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