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A reduced residue system modulo n is a set of ${\displaystyle \phi }$(n) integers such that each integer is relatively prime to n and no two are congruent modulo n. Here ${\displaystyle \phi }$ denotes Euler's totient function.

Facts

• If ${\displaystyle \{r_{1},r_{2},\dots ,r_{\varphi }(n)\}}$ is a reduced residue system with n > 2, then ${\displaystyle \sum r_{i}\equiv 0{\pmod {n}}}$.

See also

• Residue number system

External links

• Reduced residue system at MathWorld

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