# Relationships via modulo arithmetic.

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

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

$y\equiv x \pmod{35}$

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

Adding, we get

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

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

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

$y\equiv x \pmod{35}$

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

Adding, we get

$x\equiv z \pmod{35}$

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