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KoMaL A Problems
KoMaL A Problems 2023/2024
A. 858
5 variables, 2 equations, 1 solution
5 variables, 2 equations, 1 solution
Source: Komal A858
October 11, 2023
number theory
Diophantine equation
Quadratic Residues
komal
Problem Statement
Prove that the only integer solution of the following system of equations is
u
=
v
=
x
=
y
=
z
=
0
u=v=x=y=z=0
u
=
v
=
x
=
y
=
z
=
0
:
u
v
=
x
2
−
5
y
2
,
(
u
+
v
)
(
u
+
2
v
)
=
x
2
−
5
z
2
uv=x^2-5y^2, (u+v)(u+2v)=x^2-5z^2
uv
=
x
2
−
5
y
2
,
(
u
+
v
)
(
u
+
2
v
)
=
x
2
−
5
z
2
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