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Junior Balkan MO
2005 Junior Balkan MO
4
4
Part of
2005 Junior Balkan MO
Problems
(1)
\overline{abc} = abc(a+b+c) in decimal base
Source: JBMO 2005, Problem 4
10/29/2005
Find all 3-digit positive integers
a
b
c
‾
\overline{abc}
ab
c
such that
a
b
c
‾
=
a
b
c
(
a
+
b
+
c
)
,
\overline{abc} = abc(a+b+c) ,
ab
c
=
ab
c
(
a
+
b
+
c
)
,
where
a
b
c
‾
\overline{abc}
ab
c
is the decimal representation of the number.
number theory proposed
number theory