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National and Regional Contests
Belgium Contests
Flanders Math Olympiad
1999 Flanders Math Olympiad
1
6-digit number
6-digit number
Source:
August 9, 2004
LaTeX
modular arithmetic
number theory
Problem Statement
Determine all 6-digit numbers
(
a
b
c
d
e
f
)
(abcdef)
(
ab
c
d
e
f
)
so that
(
a
b
c
d
e
f
)
=
(
d
e
f
)
2
(abcdef) = (def)^2
(
ab
c
d
e
f
)
=
(
d
e
f
)
2
where
(
x
1
x
2
.
.
.
x
n
)
\left( x_1x_2...x_n \right)
(
x
1
x
2
...
x
n
)
is no multiplication but an n-digit number.
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