This is an RSA question, given data encrypted with a public key from an unknown RSA certificate of 2048 bit, let $X$ be the encrypted data, $M$ the unencrypted data, $c$ the public exponent and $N$ it's modulus. Knowing $X$, $M$ and $c$, can you deduce $N$?
$$ X = M^c \mod N $$
You can have as many $M$ and corresponding $X$ as you want, hence:
$$ X_1 = M_1^c \mod N \\ X_2 = M_2^c \mod N \\ \dots $$
I want to know if this is possible, mathematically and programatically. A brute force won't work here. Any ideas?