My way (**D2**):

Given (i) **a^2+b=2016**

and (ii) ** ****a+b=n^2**

we get **a*(a-1)= 2016-
n^2 (ii)-(i)**

since both **a*(a-1)**
and **2016** are even **n** must be even as well

clearly **n** is in the **2 to 44** range

Checking for what **even n** in this range

**(2016- n^2)/2** equals
a triangular number

We get **(a, b, n)=(32, 992,3 2)** as a solution

Tools used: Calculator and a list of triangular numbers.