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Vietnam National Olympiad
1978 Vietnam National Olympiad
1
find all three digit numbers abc such that 2(abc) = bca + cab
find all three digit numbers abc such that 2(abc) = bca + cab
Source: Vietnam MO 1978 P1
July 29, 2018
number theory
Digits
equation
Problem Statement
Find all three digit numbers
a
b
c
‾
\overline{abc}
ab
c
such that
2
⋅
a
b
c
‾
=
b
c
a
‾
+
c
a
b
‾
2 \cdot \overline{abc} = \overline{bca} + \overline{cab}
2
⋅
ab
c
=
b
c
a
+
c
ab
.
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