$\left[\begin{array}{l}\text { Factorization } \\ {[\underline{\text { Modular Arithmetic (other) })]}]}\end{array}\right.$

What remainders can be obtained when dividing $n^{3}+3$ by $n+1$ for a natural number $n>2$?
Find a number close to $n^{3}+3$ that is divisible by $n+1$.

## Solution

$n^{3}+3=(n+1)\left(n^{2}-n+1\right)+2$.

## Answer

Only 2.