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Reduced residue system: Difference between revisions

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==Facts== ==Facts==
*If {''r''<sub>1</sub>, ''r''<sub>2</sub>, ... , ''r''<sub><math>\phi</math>(''n'')</sub>} is a reduced residue system with ''n'' > 2, then <math>\sum r_i=0</math> (mod ''n''). *If <math>\{ r_1, r_2, \dots, r_\varphi(n) \}</math> is a reduced residue system with ''n'' > 2, then <math>\sum r_i \equiv 0 \pmod n</math>.


==See also== ==See also==
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==External links== ==External links==
* at MathWorld * at MathWorld




{{math-stub}} {{math-stub}}

Revision as of 16:32, 30 January 2008

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

Facts

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

See also

External links

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