# Relationships via modulo arithmetic.

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• Oct 15th 2011, 09:25 PM
MathsNewbie0811
Relationships via modulo arithmetic.
Please assist me in solving this question. Thanks.
• Oct 15th 2011, 10:35 PM
alexmahone
Re: Relationships via modulo arithmetic.
i) If $\displaystyle 5 | x - y$ and $\displaystyle 7 | x - y$, then $\displaystyle 35 | x - y$.

ii) Symmetric: If $\displaystyle x\equiv y \pmod{35}$,

$\displaystyle y\equiv x \pmod{35}$

Transitive: If $\displaystyle x\equiv y \pmod{35}$ and $\displaystyle y\equiv z \pmod{35}$,

Adding, we get

$\displaystyle x\equiv z \pmod{35}$
• Oct 15th 2011, 11:53 PM
Deveno
Re: Relationships via modulo arithmetic.
Quote:

Originally Posted by alexmahone
i) If $\displaystyle 5 | x - y$ and $\displaystyle 7 | x - y$, then $\displaystyle 35 | x - y$.

ii) Symmetric: If $\displaystyle x\equiv y \pmod{35}$,

$\displaystyle y\equiv x \pmod{35}$

Transitive: If $\displaystyle x\equiv y \pmod{35}$ and $\displaystyle y\equiv z \pmod{35}$,

Adding, we get

$\displaystyle x\equiv z \pmod{35}$

note that (i) holds only because gcd(5,7) = 1.