nameless (from idekCTF2021)

You can calculate (p+q)^2, (p-q)^2
because (p+q)^2 = p^2+q^2+2pq = p^2+q^2+2n
and      (p-q)^2 = p^2+q^2-2pq = p^2+q^2-2n.

Once you know the two values above, you can easily calculate p, q.

Please check the code for detailed implementation.

Original writeup (https://github.com/heabiside/Crypto_writeups/tree/master/nameless).