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Eotvos Mathematical Competition (Hungary)
1926 Eotvos Mathematical Competition
1
1
Part of
1926 Eotvos Mathematical Competition
Problems
(1)
x + y + 2z + 2t = a, 2x - 2y + z- t = b , NT system
Source: Eotvos 1926 p1
9/10/2024
Prove that, if
a
a
a
and
b
b
b
are given integers, the system of equatìons
x
+
y
+
2
z
+
2
t
=
a
x + y + 2z + 2t = a
x
+
y
+
2
z
+
2
t
=
a
2
x
−
2
y
+
z
−
t
=
b
2x - 2y + z- t = b
2
x
−
2
y
+
z
−
t
=
b
has a solution in integers
x
,
y
,
z
,
t
x, y,z,t
x
,
y
,
z
,
t
.
diophantine
Diophantine equation
system of equations
System
number theory