Competition problem — Number theory

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Number theory Difficulty 5.3 AIME, harder Find the answer

6. For which values of $a$ , does the congruence equation $x^{3} \equiv a(\bmod 9)$ have a solution?

Your answer

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

Solution

6. $a \equiv 0, \pm 1(\bmod 9)$ .

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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.