divisibility

Which one of the following numbers is exactly divisible by $\left(11^{13}+1\right) ?$

For what values of k given below is $\frac{(k+2)^2}{k-3}$ an integer?

For what values of k given below is $${{{{\left( {k + 2} \right)}^2}} \over {k - 3}}$$ an integer?