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2
1/(x+2)+1/(y+2)=1/2 +1/(z+2)
1/(x+2)+1/(y+2)=1/2 +1/(z+2)
Source: Switzerland - Swiss TST 1998 p2
February 18, 2020
diophantine
Diophantine equation
number theory
Problem Statement
Find all nonnegative integer solutions
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of the equation
1
x
+
2
+
1
y
+
2
=
1
2
+
1
z
+
2
\frac{1}{x+2}+\frac{1}{y+2}=\frac{1}{2} +\frac{1}{z+2}
x
+
2
1
+
y
+
2
1
=
2
1
+
z
+
2
1
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