Competition problem — Number theory

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Number theory Difficulty 5.2 AIME, harder Find the answer

14. Find all solutions to the congruence equation $5^{x} \equiv 3^{x}+2(\bmod 11)$ .

Your answer

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

Solution

14. $x \equiv 1,6(\bmod 10)$ .

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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.