$$\text{Find all square numbers} S_1,S_2 \text{ such that } S_1 −S_2 = 1989$$

Question

$$\text{Find all square numbers}  S_1,S_2 \text{ such that } S_1 −S_2 = 1989$$

anonymous · Answer

$$S_1=m^2$$$$S_2=n^2$$we must have $m>n$ so let $m=n+a$ equation becomes$$2na+a^2=1989$$$$a(2n+a)=1989$$$a$ must be a divisors of  $1989$

anonymous · Answer

$$a \in \text{{1,3,9,13,17,39,51,117,153,221,663,1989}}$$for example $a=13$ gives $n=70$ and that will gives  $m=83$ we must check all of them :)

anonymous · Answer

this is a proper solution laid out excellently thanks @mukushla 
can this be classified as diophantine

anonymous · Answer

can someone pls give a medal

anonymous · Answer

that is a quadratic diophantine equation, yes. and tnx.