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Does there exist such n? - [Bulgaria NMO 2010]
Does there exist such n? - [Bulgaria NMO 2010]
Source:
December 28, 2010
modular arithmetic
number theory proposed
number theory
Problem Statement
Does there exist a number
n
=
a
1
a
2
a
3
a
4
a
5
a
6
‾
n=\overline{a_1a_2a_3a_4a_5a_6}
n
=
a
1
a
2
a
3
a
4
a
5
a
6
such that
a
1
a
2
a
3
‾
+
4
=
a
4
a
5
a
6
‾
\overline{a_1a_2a_3}+4 = \overline{a_4a_5a_6}
a
1
a
2
a
3
+
4
=
a
4
a
5
a
6
(all bases are
10
10
10
) and
n
=
a
k
n=a^k
n
=
a
k
for some positive integers
a
,
k
a,k
a
,
k
with
k
≥
3
?
k \geq 3 \ ?
k
≥
3
?
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