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2020 China Northern MO
P5
P5
Part of
2020 China Northern MO
Problems
(1)
(a+1)/2-digit number of 2s and 0s
Source: 2020 China North Mathematical Olympiad Advanced Level P5
8/4/2020
Find all positive integers
a
a
a
so that for any
⌊
a
+
1
2
⌋
\left \lfloor \frac{a+1}{2} \right \rfloor
⌊
2
a
+
1
⌋
-digit number that is composed of only digits
0
0
0
and
2
2
2
(where
0
0
0
cannot be the first digit) is not a multiple of
a
a
a
.
number theory
Digits
multiple