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Bulgaria National Olympiad
1966 Bulgaria National Olympiad
Problem 1
3x(x-3y)=y^2+z^2 over Z (Bulgaria 1966 P1)
3x(x-3y)=y^2+z^2 over Z (Bulgaria 1966 P1)
Source:
June 23, 2021
number theory
Diophantine equation
Problem Statement
Prove that the equation
3
x
(
x
ā
3
y
)
=
y
2
+
z
2
3x(x-3y)=y^2+z^2
3
x
(
x
ā
3
y
)
=
y
2
+
z
2
doesn't have any integer solutions except
x
=
0
,
y
=
0
,
z
=
0
x=0,y=0,z=0
x
=
0
,
y
=
0
,
z
=
0
.
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