Relationships via modulo arithmetic.

**MathsNewbie0811** · October 15th 2011, 09:25 PM

Please assist me in solving this question. Thanks.

**alexmahone** · October 15th 2011, 10:35 PM

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

$x\equiv z \pmod{35}$

**Deveno** · October 15th 2011, 11:53 PM

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.

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