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Balkan MO Shortlist
2020 Balkan MO Shortlist
N1
Number Theory
Number Theory
Source: Balkan MO Shortlist 2020 N1
September 14, 2021
number theory
Problem Statement
Determine all positive integers
n
n
n
such that
a
2
+
n
2
b
2
−
n
2
\frac{a^2+n^2}{b^2-n^2}
b
2
−
n
2
a
2
+
n
2
is a positive integer for some
a
,
b
∈
N
a,b\in \mathbb{N}
a
,
b
∈
N
.
T
u
r
k
e
y
Turkey
T
u
r
k
ey
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