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5x = 0 (mod 6)

I don't even know where to begin.

Ok, does 0(mod6) = 0mod6?

0/6 always give 0 so is the answer x=0?

I don't have any clue.

  • 0
    An answer is $0$, but note that $5\times 6 = 30 \equiv 0 \pmod 6$ so $6$ is also a solution and there are many more.2012-10-27
  • 1
    Do you know what $a=b \pmod{n}$ means?2012-10-27

2 Answers 2

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Recall that if $a \vert (bc)$ and $(a,b)=1$, then $a \vert c$.

In your case, note that $6 \vert (5x)$ and $(6,5) = 1$. Hence, $6 \vert x$ i.e. $x \equiv 0 \pmod 6$

  • 0
    Should the symbol be ≡ instead of =?2012-10-27
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Hint $\rm\,\ mod\ 6\!:\,\ 6x,5x\equiv 0\:\Rightarrow\:x = 6x\!-\!5x\equiv 0,\:$ and conversely.