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Poland - Second Round
2014 Poland - Second Round
1.
Prove that y|x^2
Prove that y|x^2
Source: Poland 2014 - Second Round P1
July 28, 2019
number theory
Problem Statement
Let
x
,
y
x, y
x
,
y
be positive integers such that
x
2
y
+
y
2
x
\frac{x^2}{y}+\frac{y^2}{x}
y
x
2
+
x
y
2
is an integer. Prove that
y
∣
x
2
y|x^2
y
∣
x
2
.
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