1980 AMC 12 第 28 题
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28.
当 等于下列哪个数时，多项式 不能被 整除？
The polynomial is not divisible by if equals
小提示：
把非实三次单位根 代入该多项式
Evaluate the polynomial at a nonreal cube root of unity
大提示：
利用 ，并按 模 的余数分类
Use and consider modulo
解答：
令 。由于 ，把 代入多项式可得 该式通常为 ；仅当 时，它才等于 。后一种情形恰好在 是 的倍数时发生。选项中只有 能被 整除，所以此时整除性不成立。
因此，正确答案是 C。
Let Since the polynomial evaluated at is This is unless in which case it is The latter occurs exactly when is divisible by Among the choices only is divisible by so that is the value for which divisibility fails.
Therefore, the correct answer is C.
其他年份的第 28 题
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