Why it works: Yāvadūnaṃ

For n near base B with deficiency d ($n = B-d$): $n^2 = (B-d)$² = $B^2-2Bd+d^2 = B$($B-2d$)+$d^2 = B$($n-d$)+d². Left part = $n-d = B-2d$; right part = d². Above base: $n = B+d \to n^2 = B$($n+d$)+d².