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

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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.