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Contests
National and Regional Contests
Azerbaijan Contests
Azerbaijan IZHO TST
2020 Azerbaijan IZHO TST
6
6
Part of
2020 Azerbaijan IZHO TST
Problems
(1)
Sequence problem
Source: Azerbaijan Math Olympiad Training
12/14/2019
Define a sequence
a
n
n
≥
1
{{a_n}}_{n\ge1}
a
n
n
≥
1
such that
a
1
=
1
a_1=1
a
1
=
1
,
a
2
=
2
a_2=2
a
2
=
2
and
a
n
+
1
a_{n+1}
a
n
+
1
is the smallest positive integer
m
m
m
such that
m
m
m
hasn't yet occurred in the sequence and also
g
c
d
(
m
,
a
n
)
≠
1
gcd(m,a_n)\neq{1}
g
c
d
(
m
,
a
n
)
=
1
. Show that all positive integers occur in the sequence.
number theory
TST