There is no barrier to stop a clever girl!

Challenge

This is basically a normal RSA, with some condition for the primes

It's quite unlikely that the fraction simplifies so we simply assume we have 2 equations:

\begin{align*} 2s-X &= 2N + p + q + 1\\\\ s+Y &= N + q \end{align*}

Simplifying this to solve for the primes, we get

\begin{align*} 2Y + X &= q - p + 1\\\\ (2Y + X - 1)q &= q^2 - N \end

and the quadratic can easily be solved for , thus can also easily be solved

Getting the flag

Since e=0x20002, we calculate m^2 by using e=0x10001, then using CRT, we compute m mod p and m mod q and find m mod N

mp = mod(m2,p).sqrt()
mq = mod(m2,q).sqrt()
m = crt([int(mp),int(mq)],[p,q])