Competition problem — Number theory

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Number theory Difficulty 5.2 AIME, harder Find the answer

15. 对哪些整数 $a$ , 同余方程 $10^{x} \equiv a(\bmod 41)$ 有解?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

15. $a \equiv 1,10,16,18,37(\bmod 41)$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.