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National and Regional Contests
Serbia Contests
Serbia Team Selection Test
1987 Yugoslav Team Selection Test
Problem 1
Problem 1
Part of
1987 Yugoslav Team Selection Test
Problems
(1)
NT recurrence, condition for 7|x_n
Source: Yugoslav TST 1987 P1
5/28/2021
Let
x
0
=
a
,
x
1
=
b
x_0=a,x_1=b
x
0
=
a
,
x
1
=
b
and
x
n
+
1
=
2
x
n
−
9
x
n
−
1
x_{n+1}=2x_n-9x_{n-1}
x
n
+
1
=
2
x
n
−
9
x
n
−
1
for each
n
∈
N
n\in\mathbb N
n
∈
N
, where
a
,
b
a,b
a
,
b
are integers. Find the necessary and sufficient condition on
a
a
a
and
b
b
b
for the existence of an
x
n
x_n
x
n
which is a multiple of
7
7
7
.
recurrence relation
number theory
Sequences