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Paraguay Contests
Paraguay Mathematical Olympiad
2012 Paraguay Mathematical Olympiad
4
4
Part of
2012 Paraguay Mathematical Olympiad
Problems
(1)
Problem 4
Source: Paraguayan Mathematical Olympiad 2012
10/15/2012
Find all four-digit numbers
a
b
c
d
‾
\overline{abcd}
ab
c
d
such that they are multiples of
3
3
3
and that
a
b
‾
−
c
d
‾
=
11
\overline{ab}-\overline{cd}=11
ab
−
c
d
=
11
. (
a
b
c
d
‾
\overline{abcd}
ab
c
d
is a four-digit number;
a
b
‾
\overline{ab}
ab
is a two digit-number as
c
d
‾
\overline{cd}
c
d
is).
number theory proposed
number theory