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Ireland National Math Olympiad
2021 Irish Math Olympiad
3
3
Part of
2021 Irish Math Olympiad
Problems
(1)
n + T(n) = 10n, whereT(n) sends first 2 digits to the end
Source: 2021 Irish Mathematical Olympiad P3
5/30/2021
For each integer
n
≥
100
n \ge 100
n
≥
100
we define
T
(
n
)
T(n)
T
(
n
)
to be the number obtained from
n
n
n
by moving the two leading digits to the end. For example,
T
(
12345
)
=
34512
T(12345) = 34512
T
(
12345
)
=
34512
and
T
(
100
)
=
10
T(100) = 10
T
(
100
)
=
10
. Find all integers
n
≥
100
n \ge 100
n
≥
100
for which
n
+
T
(
n
)
=
10
n
n + T(n) = 10n
n
+
T
(
n
)
=
10
n
.
number theory
Digits
decimal representation