It is easy to have Java produce a list of quadratic
residues by automating the method used in the Prelab section.
Specifically, the applet below computes a2 % n
for each value of a satisfying gcd(a, n) = 1
and 1 
a
n. The resulting output contains the quadratic residues.
Try it out:
In the very near future, you will want to count the number of quadratic residues modulo a prime. You can do so using a modified version of the previous applet that includes the number of quadratic residues in the list, thus avoiding the tedium of counting them yourself.
Research Question 1
If p is an odd prime, how many quadratic residues
are there mod p?
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