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Problem 415

AMC 12 late, AIME early

Number theory Difficulty 4.8 Find the answer

For which modulus do the numbers 1 and 5 form a reduced residue system?

Your answer

Official solution

From the condition, we can see that $\varphi(n)=2$ . This equation has three solutions: $n=3,4,6$ . However, $1 \equiv 5(\bmod 4)$ , so the answers are only the numbers 3 and 6.

## Answer

For moduli 3 and 6.

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