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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2023 Moldova Team Selection Test
12
12
Part of
2023 Moldova Team Selection Test
Problems
(1)
Arithmetic sequence
Source: Mathematics and Youth Magazine (vietnam)
9/16/2020
The sequence
(
a
n
)
\left(a_n \right)
(
a
n
)
is defined by
a
1
=
1
,
a
2
=
2
a_1=1, \ a_2=2
a
1
=
1
,
a
2
=
2
and
a
n
+
2
=
2
a
n
+
1
−
p
a
n
,
∀
n
≥
1
,
a_{n+2} = 2a_{n+1}-pa_n, \ \forall n \ge 1,
a
n
+
2
=
2
a
n
+
1
−
p
a
n
,
∀
n
≥
1
,
for some prime
p
.
p.
p
.
Find all
p
p
p
for which there exists
m
m
m
such that
a
m
=
−
3.
a_m=-3.
a
m
=
−
3.
number theory
arithmetic sequence