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Baltic Way
2013 Baltic Way
19
19
Part of
2013 Baltic Way
Problems
(1)
Recursion
Source: 2013 Baltic Way, Problem 19
12/31/2013
Let
a
0
a_0
a
0
be a positive integer and
a
n
=
5
a
n
−
1
+
4
a_n=5a_{n-1}+4
a
n
=
5
a
n
−
1
+
4
for all
n
≥
1
n\ge 1
n
≥
1
. Can
a
0
a_0
a
0
be chosen so that
a
54
a_{54}
a
54
is a multiple of
2013
2013
2013
?
algebra
polynomial
modular arithmetic
number theory unsolved
number theory