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Paraguay Mathematical Olympiad
2010 Paraguay Mathematical Olympiad
4
4
Part of
2010 Paraguay Mathematical Olympiad
Problems
(1)
Paraguayan National Olympiad 2010, Level 3, Problem 4
Source:
9/20/2014
Find all 4-digit numbers
a
b
c
d
‾
\overline{abcd}
ab
c
d
that are multiples of
11
11
11
, such that the 2-digit number
a
c
‾
\overline{ac}
a
c
is a multiple of
7
7
7
and
a
+
b
+
c
+
d
=
d
2
a + b + c + d = d^2
a
+
b
+
c
+
d
=
d
2
.