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水一个跨年题

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Czhang271828 posted 2022-12-31 19:12 |Read mode

记 $\overline {xyz}$ 为三位数 $100x+10y+z$. 求以下整数方程 ($a,b,c,d\in \{0,1,\ldots, 9\}$)
\[
(a+b+c+d)(a^2+b^2+c^2+d^2)^2=\overline{abcd}.
\]

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超级神童！ posted 2022-12-31 19:37

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力工 posted 2022-12-31 19:35

2023

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只有 2023 和 2400 两个解。 posted 2022-12-31 20:07

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hbghlyj posted 2022-12-31 21:47

5进制下3100
9进制下4210
10进制下2023, 2400
13进制下5031
16进制下8000

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original poster Czhang271828 posted 2023-1-6 18:53

mp.weixin.qq.com/s/eU00x0BKBDoFq3uUhc2Ekg
(转)

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isee posted 2023-1-6 23:50

这个题不错啊，限定下只有一个解的话

isee=freeMaths@知乎

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