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[数论] 映射 x↦x^3 是否是双射

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hbghlyj Posted at 2024-10-21 23:59:54 |Read mode

Last edited by hbghlyj at 2024-10-29 20:25:00有限域中的映射 x↦x^3 是否是双射?

参见 Paulo Ribenboim 所著《13 Lectures on Fermat’s Last Theorem》第 12 讲

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Author| hbghlyj Posted at 2024-10-22 15:10:24

例子

在 $\mathbb F_{17}$ 上检查它是否是双射：

x	x^3
0	0
1	1
2	8
3	10
4	13
5	6
6	12
7	3
8	2
9	15
10	14
11	5
12	11
13	4
14	7
15	9
16	16

所以它是双射。

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Author| hbghlyj Posted at 2024-10-30 04:25:38

那么一般情况呢

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