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Kyiv Mathematical Festival
2016 Kyiv Mathematical Festival
P1
P1
Part of
2016 Kyiv Mathematical Festival
Problems
(1)
equation with fractions
Source: Kyiv mathematical festival 2016
5/8/2016
Prove that for every positive integers
a
a
a
and
b
b
b
there exist positive integers
x
x
x
and
y
y
y
such that
x
y
+
a
+
y
x
+
b
=
3
2
.
\dfrac{x}{y+a}+\dfrac{y}{x+b}=\dfrac{3}{2}.
y
+
a
x
+
x
+
b
y
=
2
3
.
equation
Kyiv mathematical festival
algebra