(In reply to two computer solutions
I wrote an "even aquare" meaning a square of an integer,
NOT NECESSARILY EVEN INTEGER.
the solution I had in mind was 183184, .
since you added 715716.- i looked for additional answers,
disregarding parity of the candidate solutions (mod2=0 in your program).
There are indeed 2 odd answers : 328329 and 528529.
Nothing wrong with your interpretation , just wanted to let you know.