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4
Silk Road 2021 P4
Silk Road 2021 P4
Source:
June 28, 2021
number theory
Problem Statement
Integers
x
,
y
,
z
,
t
x,y,z,t
x
,
y
,
z
,
t
satisfy
x
2
+
y
2
=
z
2
+
t
2
x^2+y^2=z^2+t^2
x
2
+
y
2
=
z
2
+
t
2
and
x
y
=
2
z
t
xy=2zt
x
y
=
2
z
t
prove that
x
y
z
t
=
0
xyzt=0
x
yz
t
=
0
Proposed by
M
.
A
b
d
u
v
a
l
i
e
v
M. Abduvaliev
M
.
A
b
d
uv
a
l
i
e
v
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