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2021 Malaysia IMONST 1
10
(x - y)^2 + (y + z)^2 = (x + y)^2 + (y- z)^2 2021 Malaysia IMONST 1 Senior P10
(x - y)^2 + (y + z)^2 = (x + y)^2 + (y- z)^2 2021 Malaysia IMONST 1 Senior P10
Source:
September 21, 2021
Diophantine equation
diophantine
number theory
Problem Statement
Determine the number of integer solutions
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
, with
0
≤
x
,
y
,
z
≤
100
0 \le x, y, z \le 100
0
≤
x
,
y
,
z
≤
100
, for the equation
(
x
−
y
)
2
+
(
y
+
z
)
2
=
(
x
+
y
)
2
+
(
y
−
z
)
2
.
(x - y)^2 + (y + z)^2 = (x + y)^2 + (y - z)^2.
(
x
−
y
)
2
+
(
y
+
z
)
2
=
(
x
+
y
)
2
+
(
y
−
z
)
2
.
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