## Largest value of $n$

### Largest value of $n$

Find the largest value of $n$ such that $n^3+10$ is divisible by $n+10$.

Every logical solution to a problem has its own beauty.

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**Important**: Please make sure that you have read about the**Rules, Posting Permissions and Forum Language**)### Re: Largest value of $n$

*"Go down deep enough into anything and you will find mathematics." ~Dean Schlicter*

### Re: Largest value of $n$

I didn't understand the sign $||$ here, because it is used to mean:If $p^a||n$,then $p^{a+1}$ does not divide $n$

However,it was a problem from AIME may be and simialr to my post"find the largest $x$'

$n+10|n^3+10$ and $n^3+100$,then $n+10|990,n_{max}=980$

However,it was a problem from AIME may be and simialr to my post"find the largest $x$'

$n+10|n^3+10$ and $n^3+100$,then $n+10|990,n_{max}=980$

One one thing is neutral in the universe, that is $0$.

### Re: Largest value of $n$

That was a typo. Sorry!

*"Go down deep enough into anything and you will find mathematics." ~Dean Schlicter*

### Re: Largest value of $n$

Solu ta ki?

**A man is not finished when he's defeated, he's finished when he quits.**

### Re: Largest value of $n$

a nice problem!Zzzz wrote:Find the largest value of $n$ such that $n^3+10$ is divisible by $n+10$.

**A man is not finished when he's defeated, he's finished when he quits.**