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Vojtěch Jarník IMC
1996 VJIMC
Problem 3
finite number of solutions to a diophantine equation
finite number of solutions to a diophantine equation
Source: VJIMC 1996 1.3
October 13, 2021
Diophantine equation
number theory
Problem Statement
Prove that the equation
x
1
+
x
2
+
y
1
+
y
2
+
z
1
+
z
2
=
1
1996
\frac x{1+x^2}+\frac y{1+y^2}+\frac z{1+z^2}=\frac1{1996}
1
+
x
2
x
+
1
+
y
2
y
+
1
+
z
2
z
=
1996
1
has finitely many solutions in positive integers.
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