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Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2019 Junior Balkan Team Selection Tests - Moldova
12
Moldova JTST 2019 P12
Moldova JTST 2019 P12
Source:
April 19, 2019
combinatorics
Problem Statement
The number
B
=
a
1
a
2
…
a
n
a
1
a
2
…
a
n
‾
B=\overline{a_1a_2\dots a_na_1a_2\dots a_n}
B
=
a
1
a
2
…
a
n
a
1
a
2
…
a
n
it is called
r
e
p
e
t
i
t
i
o
n
repetition
re
p
e
t
i
t
i
o
n
of the natural positive number
A
=
a
1
a
2
…
a
n
‾
A = \overline{a_1a_2\dots a_n}
A
=
a
1
a
2
…
a
n
.Prove that there is an infinity of natural numbers ,whose
r
e
p
e
t
i
t
i
o
n
repetition
re
p
e
t
i
t
i
o
n
is a perfect square .
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