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Question Number 63689 by Rio Michael last updated on 07/Jul/19
Show that  if  a∣b  then an∣bn
$${Show}\:{that}\:\:{if}\:\:{a}\mid{b}\:\:{then}\:{an}\mid{bn} \\ $$
Commented by Prithwish sen last updated on 07/Jul/19
lf a∣b  then b=aq   (q∈N )  multiplying both sides by n  bn = anq ⇒ ((bn)/(an)) = q ⇒ an∣bn   Hence proved.
$$\mathrm{lf}\:\mathrm{a}\mid\mathrm{b} \\ $$$$\mathrm{then}\:\mathrm{b}=\mathrm{aq}\:\:\:\left(\mathrm{q}\in\mathrm{N}\:\right) \\ $$$$\mathrm{multiplying}\:\mathrm{both}\:\mathrm{sides}\:\mathrm{by}\:\mathrm{n} \\ $$$$\mathrm{bn}\:=\:\mathrm{anq}\:\Rightarrow\:\frac{\mathrm{bn}}{\mathrm{an}}\:=\:\mathrm{q}\:\Rightarrow\:\mathrm{an}\mid\mathrm{bn}\: \\ $$$$\mathrm{Hence}\:\mathrm{proved}. \\ $$
Commented by Rio Michael last updated on 07/Jul/19
correct
$${correct} \\ $$
Commented by Prithwish sen last updated on 07/Jul/19
thanks
$$\mathrm{thanks} \\ $$

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