# Describing a sequence of terms

I'm currently in a Discrete Mathematics class in college, and my professor is giving a quiz soon and told us what will be on it.

Problem is, I missed a day of class and I have no idea to figure out what he was saying when he gave us this problem:

Describe the sequence $X_{n+1} = (Ax_n + b) \mod p$

Is there a common name for this / what am I supposed to do here? I've done a couple of google searches but found nothing; I was hoping some of you might be able to clarify what this means.

Edit: I think $p$ is meant to be interpreted as a prime number.

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The person may have been discussing the Linear Congruential Generators. With suitable choice of parameters, these are a simple method to generate a pseudo-random sequence. Of course such a sequence is definitely not "random," since it is periodic. But if the period is extremely long, say of length $\approx 10^{100}$, the periodicity is not a practical drawback.
@BenjaminKovach: If the parameters $A$, $b$, and $p$ were explicitly given, with $p$ at least quite small, writing down a full period may have been intended. Otherwise, I really can't guess what the instructor was asking for. – André Nicolas Nov 15 '12 at 16:33
I really don’t know what he’s looking for. About all that you can say without further information is that the sequence is periodic. If $A$ is a multiple of $p$, the sequence is constant: $x_n=b\bmod p$ for every $n$ except perhaps the initial value. If $A$ is not a multiple of $p$, the sequence is periodic with period $p$ and runs through the values $0,1,\dots,p-1$ in some order. (Here I’m assuming that $p$ is intended to be a prime.)
I'm guessing that p is supposed to be a prime number as well, if that matters. This might be sufficient too; I understand what you're saying and that makes sense. Thanks for your response! – Benjamin Kovach Nov 15 '12 at 16:08
@Benjamin: You’re welcome! I should have said that I was assuming in my response that $p$ was prime; I’ll add that now. – Brian M. Scott Nov 15 '12 at 16:10