RSA: Know the public key from a pair of plain text and their cipher? I have two plain texts files cipher with RSA (with the same public and private key) and I have their cipher texts too. Would it be possible know the public key from that information?

My messages have 10 characters and I cannot calculate a huge exponential operation. No padding is used on the messages before encryption.
From a couple of plaintext/ciphertext $(m_1, c_1)$ and $(m_2, c_2)$, then the modulus $n$ is a factor of
$$
\gcd(m_1^e-c_1, m_2^e-c_2).
$$
The explanation is that
$$
c_i = m_i^e - \lambda_i n
$$
for some unknown $\lambda_i$, so $n$ both divides $m_1^e-c_1$ and $m_2^e-c_2$.

Of course, this solution works if you know $e$, but it can be tried with some classically used values ($e=3$ for instance).