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2019 Cono Sur Olympiad
2
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Part of
2019 Cono Sur Olympiad
Problems
(1)
2019 Cono Sur Mathematical Olympiad, P2
Source:
8/28/2019
We say that a positive integer
M
M
M
with
2
n
2n
2
n
digits is hypersquared if the following three conditions are met:[*]
M
M
M
is a perfect square. [*]The number formed by the first
n
n
n
digits of
M
M
M
is a perfect square. [*]The number formed by the last
n
n
n
digits of
M
M
M
is a perfect square and has exactly
n
n
n
digits (its first digit is not zero).Find a hypersquared number with
2000
2000
2000
digits.
number theory
Digits