uniqueness of the RSA public modulus What is the probability that two separate RSA public moduli are the same? For example, consider a 2048-bit modulus. The number seems to be huge, but the choice for prime factors p and q is much more restrictive: They both should be 1024-bit in size, not too close to $\sqrt{p*q}$ and the most significant bit should remain set. Even if $2^{1023}$ seems like a lot of numbers, not every integer in this set suits the RSA scheme.
Since public exponent $e$ should be set to $0x010001$, if I find a collision for the RSA modulus, have I also found a collision for the RSA private exponent?
Is it possible to treat the public RSA components (e.g. represented as $H(modulus, exponent)$) as a unique value for identification purposes?
If the RSA keys were generated randomly, then it is inconceivable that two different devices would happen to pick the same key.

Taking 2048 bit RSA keys as an example, there are approximately $2^{1014}$ 1024 bit primes; if we consider them pairwise (and realise that about half the pairs yield a 2047 bit number), that means there are about $2^{2026}$ RSA modulii possible.

This is an incredibly huge number.  Even if we take into account the fact that the probability for generating each modulii isn't precisely the same (depending on the actual algorithm used), it'd be far more likely that you'd win the lottery 100 times in a row than two devices happen to pick the same RSA key.

On the other hand, examples of devices having the same RSA key have been seen.  In this case, the problem wasn't that someone won the lottery 100 times; instead, they got the random part wrong.

An essential part of the above argument is that we pick them randomly; that is, we start with a 'random' value, and we use that value to select two primes.  If two different devices start with the same 'random' value, and use the same algorithm to select the primes, they'll end up with the same RSA key.

So, to answer your question: whether you can assume that two different devices always have different keys, well, that depends on whether whoever did generate the keys had proper amounts of randomness (entropy) when doing so.  If they did, you can certainly assume it; if they're broken, any such assumption is suspect.