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Find out the greatest integer $n$ for which $n^3+500$ will be divisible by $n+10$.

Please,use $Latex$ in writing equations so that the equations look beautiful.BTW,here is the solution:
$n^{3}+500=n^{3}+10^{3}-500$
$=(n+10)(n^{2}-10n+100)-500$
$(n+10)$ divides $(n+10)(n^{2}-10n+100)$.So,$(n+10)$ must divide $500$.The greatest value of $(n+10)$ which divides $500$ is $500$.$\therefore$ the greatest value of $n$ is $490$