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Junior Balkan MO
2003 Junior Balkan MO
1
1
Part of
2003 Junior Balkan MO
Problems
(1)
A+2B+4 is a perfect square
Source: JBMO 2003, Problem 1
10/10/2005
Let
n
n
n
be a positive integer. A number
A
A
A
consists of
2
n
2n
2
n
digits, each of which is 4; and a number
B
B
B
consists of
n
n
n
digits, each of which is 8. Prove that
A
+
2
B
+
4
A+2B+4
A
+
2
B
+
4
is a perfect square.