RSA Question- max number of ascii characters encrypted at one time I'm a student new to cryptography and have a fairly straight forward RSA question that I'm struggling to wrap my head around.

"Alice's RSA public key [N:e] is stored in binary as a 16bit integer &amp;: 8bit integer.

What is the maximum number of ASCII letters that can be encrypted at once and sent to Alice if assuming no padding?"

My initial thought was 1 ASCII character at a time because M &lt; N. Therefore it couldn't be 2 characters (2 x 8 bits) because M would = N.

From my understanding of modular arithmetic:
51 mod 5 = 0   But    41 mod 5 = 4

So I kind of understand that if M is equal or greater than N, I will only decrypt an equivalent message but not identical.

Could somebody explain this to me in more detail?
Don't do it!  It's a trap!  Applying the arcane mathemagical spell that is RSA trapdoor permutation to ASCII does not an encryption scheme make!  The RSA trapdoor permutation conceals uniform random elements of $\mathbb Z/n\mathbb Z$; to use it for anything else is a mistake, and a fool's errand clothed in naive textbook idealism.

It's like telling your class that modern aviation is built out of paper airplanes, except unlike the obscure mathematics of RSA, paper airplanes self-evidently cannot function like an Airbus A380 or even a Cessna C-34.  If this is how you are taught aeronautical engineering, I exhort you to find another instructor!

Real encryption schemes based on RSA use the fancy mathematics to conceal a 256-bit secret key for symmetric-key authenticated encryption such as AES-GCM, and use that to encrypt the message.

That preface said, taking your question at face value:

The space of ‘messages’ $M$ is set of the integers between $0$ and $N$.  Any other integer is equivalent, as far as RSA is concerned, to one between $0$ and $N$, because all arithmetic is modulo $N$; for example, $N + 1$ is equivalent to $1$, because they differ by a multiple of $N$.

So, for a modulus $N$ between $2^{15}$ and $2^{16}$, there are at least $2^{15}$ distinct messages.  How many ASCII characters are there?  How many pairs of ASCII characters are there?