RSA: Derive modulus from known ciphertexts encoded with same keypairs I have two ciphertexts

$c_1 = m_1^e \bmod n$

$c_2 = m_2^e \bmod n$

I know $c_1, c_2, m_1, m_2$ and $e$. Is there a way to derive n from this? I first thought Franklin Reiter but I'd need an $n$ for that which is precisely what I am missing. What other approaches are there?
Here is the hint you requested:


We know that we have $m_1^e - c_1 = k_1n$ for some integer $k_1$
We know that we have $m_2^e - c_2 = k_2n$ for some integer $k_2$


So, given that we know the values $k_1n$ and $k_2n$, how can we recover the common $n$ value?  Hint: look at the $\gcd$ function...