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Greece Junior Math Olympiad
2018 Greece Junior Math Olympiad
3
3
Part of
2018 Greece Junior Math Olympiad
Problems
(1)
Integer fraction implies perfect square
Source: Greece JMO 2018, pr 3
3/5/2018
Let
a
a
a
and
b
b
b
be positive integers with
b
b
b
odd, such that the number
(
a
+
b
)
2
+
4
a
a
b
\frac{(a+b)^2+4a}{ab}
ab
(
a
+
b
)
2
+
4
a
is an integer. Prove that
a
a
a
is a perfect square.
number theory
Perfect Square