#### bosman3321

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- Thread starter bosman3321
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If \(\displaystyle n \) is a multiple of \(\displaystyle m \) then \(\displaystyle \exists k\in\mathbb{Z}^+ \) such that \(\displaystyle km=n\).

If \(\displaystyle m \) is a multiple of \(\displaystyle n \) then \(\displaystyle \exists j\in\mathbb{Z}^+ \) such that \(\displaystyle jn=m\).

Please finish the proof an post the result.

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I dont know how to.If \(\displaystyle n \) is a multiple of \(\displaystyle m \) then \(\displaystyle \exists k\in\mathbb{Z}^+ \) such that \(\displaystyle km=n\).

If \(\displaystyle m \) is a multiple of \(\displaystyle n \) then \(\displaystyle \exists j\in\mathbb{Z}^+ \) such that \(\displaystyle jn=m\).

Please finish the proof an post the result.

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Suppose that \(\displaystyle m\text{ is a multiple of }n~\&~ n\text{ is a multiple of }m\).I dont know how to.

So \(\displaystyle \exists K\in\mathbb{Z}^+[K\cdot n=m]~\&~\exists J\in\mathbb{Z}^+[J\cdot m=n] \)

\(\displaystyle \therefore,\; \)

So it must be the case that:

\(\displaystyle \begin{align*}m&=K\cdot n \\&=K\cdot(J\cdot m)\\&=(K\cdot J)\cdot m \\\large1 &= K\cdot J \end{align*}\)

\(\displaystyle \LARGE\text{Now what?}\)

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ThanksIf \(\displaystyle n \) is a multiple of \(\displaystyle m \) then \(\displaystyle \exists k\in\mathbb{Z}^+ \) such that \(\displaystyle km=n\).

If \(\displaystyle m \) is a multiple of \(\displaystyle n \) then \(\displaystyle \exists j\in\mathbb{Z}^+ \) such that \(\displaystyle jn=m\).

Please finish the proof an post the result.

Got it

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You were helped showing that if m and n are multiples of another then m=n. Did you show that if m=n, then m and n are multiples of one another? It is extremely easy but needs to be shown.Thanks

Got it