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National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2024 Korea Junior Math Olympiad (First Round)
17.
17.
Part of
2024 Korea Junior Math Olympiad (First Round)
Problems
(1)
Number Theory with modulars
Source: 2024 KJMO first round
10/27/2024
Find the number of
n
n
n
that follow the following:
ā
\bigstar
ā
The number of integers
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
following this equation is not a multiple of 4.
2
n
=
x
2
+
2
y
2
+
2
x
2
+
2
x
y
+
2
y
z
2n=x^2+2y^2+2x^2+2xy+2yz
2
n
=
x
2
+
2
y
2
+
2
x
2
+
2
x
y
+
2
yz
number theory
modular arithmetic