OEIS A212558: Proof of Unproven Conjecture? Proven!

[stored]

(n - s)^2 = (n + s)^2 - 4 n s = (n + s)^2 - 4 s (n + s) + 4 s^2
(n + s)^2 = (n - s)^2 + 4 n s = (n - s)^2 + 4 s (n - s) + 4 s^2

Then source problem is equivalent
4 s^2 mod (n+s) = 4 s^2 mod (n-s)

This is true for all s, that
4 s^2 < n-s.