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Romania National Olympiad
1997 Romania National Olympiad
2
a + bc is perfect square - - 1997 Romania NMO VII p2
a + bc is perfect square - - 1997 Romania NMO VII p2
Source:
August 13, 2024
number theory
Problem Statement
Let
a
≠
0
a \ne 0
a
=
0
be a natural number. Prove that
a
a
a
is a perfect square if and only if for every
b
∈
N
∗
b \in N^*
b
∈
N
∗
there exists
c
∈
N
∗
c \in N^*
c
∈
N
∗
such that
a
+
b
c
a + bc
a
+
b
c
is a perfect square.
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