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International Contests
Tournament Of Towns
1994 Tournament Of Towns
(428) 5
(428) 5
Part of
1994 Tournament Of Towns
Problems
(1)
TOT 428 1994 Autumn A J5 2 periodic sequences with periods 7, 13
Source:
6/12/2024
The periods of two periodic sequences are
7
7
7
and
13
13
13
. What is the maximal length of initial sections of the two sequences which can coincide? (The period
p
p
p
of a sequence
a
1
a_1
a
1
,
a
2
a_2
a
2
,
.
.
.
...
...
is the minimal
p
p
p
such that
a
n
=
a
n
+
p
a_n = a_{n+p}
a
n
=
a
n
+
p
for all
n
n
n
.) (AY Belov)
algebra
Sequence
periodic