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2019 Iberoamerican Mathematical Olympiad, P1
2019 Iberoamerican Mathematical Olympiad, P1
Source:
September 15, 2019
number theory
Digits
Problem Statement
For each positive integer
n
n
n
, let
s
(
n
)
s(n)
s
(
n
)
be the sum of the squares of the digits of
n
n
n
. For example,
s
(
15
)
=
1
2
+
5
2
=
26
s(15)=1^2+5^2=26
s
(
15
)
=
1
2
+
5
2
=
26
. Determine all integers
n
≥
1
n\geq 1
n
≥
1
such that
s
(
n
)
=
n
s(n)=n
s
(
n
)
=
n
.
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