A question that is related to Research Question 1 is the following:

How many square roots mod

pcan an integer have?We say that

mis a square root ofamodulopifam^{2}modp. The applet below returns a list of all square roots ofamodp. For example, here are the square roots of 3 modulo 11:

You can check the results using the Java calculator:

## Research Question 2

Let

pbe an odd prime andaan integer that is not divisible byp. How many square roots canahave modulop?Once you have completed Research Question 2, you may find that you have enough information to prove your conjecture for Research Question 1. Go back, and give it a try. If you have success, great! If not, don't despair. Go on to the next section, and return to Research Question 1 later.

Section 11.1 | Section 11.2 | Section 11.3 | Section 11.4 | Section 11.5 | Section 11.6

Copyright © 2001 by W. H. Freeman and Company