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Regional Mathematical Olympiad
2023 India Regional Mathematical Olympiad
3
RMO 2023 P3
RMO 2023 P3
Source:
October 29, 2023
number theory
Problem Statement
For any natural number
n
n
n
, expressed in base 10 , let
s
(
n
)
s(n)
s
(
n
)
denote the sum of all its digits. Find all natural numbers
m
m
m
and
n
n
n
such that
m
<
n
m<n
m
<
n
and
(
s
(
n
)
)
2
=
m
and
(
s
(
m
)
)
2
=
n
.
(s(n))^2=m \text { and }(s(m))^2=n .
(
s
(
n
)
)
2
=
m
and
(
s
(
m
)
)
2
=
n
.
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