Question

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

Answer 1

\[S_1=m^2\]\[S_2=n^2\]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 \(1989\)

Answer 2

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

Answer 3

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

Answer 4

can someone pls give a medal

Answer 5

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