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Mexico Contests
Mexico National Olympiad
1989 Mexico National Olympiad
4
4
Part of
1989 Mexico National Olympiad
Problems
(1)
smallest n so that r =\overline{a_1a_0a_m ..._20} = 2n, in decimal
Source: Mexican Mathematical Olympiad 1989 OMM P4
7/27/2018
Find the smallest possible natural number
n
=
a
m
.
.
.
a
2
a
1
a
0
‾
n = \overline{a_m ...a_2a_1a_0}
n
=
a
m
...
a
2
a
1
a
0
(in decimal system) such that the number
r
=
a
1
a
0
a
m
.
.
.
2
0
‾
r = \overline{a_1a_0a_m ..._20}
r
=
a
1
a
0
a
m
..
.
2
0
equals
2
n
2n
2
n
.
number theory
decimal representation