MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN C Problems
5
C 5
C 5
Source:
May 25, 2007
analytic geometry
graphing lines
slope
conics
hyperbola
Quadratic Residues
Problem Statement
Let
p
p
p
be an odd prime and let
Z
p
Z_{p}
Z
p
denote (the field of) integers modulo
p
p
p
. How many elements are in the set
{
x
2
:
x
∈
Z
p
}
∩
{
y
2
+
1
:
y
∈
Z
p
}
?
\{x^{2}: x \in Z_{p}\}\cap \{y^{2}+1: y \in Z_{p}\}?
{
x
2
:
x
∈
Z
p
}
∩
{
y
2
+
1
:
y
∈
Z
p
}?
Back to Problems
View on AoPS