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National and Regional Contests
Saudi Arabia Contests
Saudi Arabia BMO TST
2022 Saudi Arabia BMO + EGMO TST
p1
p1
Part of
2022 Saudi Arabia BMO + EGMO TST
Problems
(1)
a_{n+1} = a_n+rad(a_n), product of all distinct prime factors
Source: 2022 Saudi Arabia March Camp Test p1 BMO + EGMO TST
5/13/2024
By
r
a
d
(
x
)
rad(x)
r
a
d
(
x
)
we denote the product of all distinct prime factors of a positive integer
n
n
n
. Given
a
∈
N
a \in N
a
∈
N
, a sequence
(
a
n
)
(a_n)
(
a
n
)
is defined by
a
0
=
a
a_0 = a
a
0
=
a
and
a
n
+
1
=
a
n
+
r
a
d
(
a
n
)
a_{n+1} = a_n+rad(a_n)
a
n
+
1
=
a
n
+
r
a
d
(
a
n
)
for all
n
≥
0
n \ge 0
n
≥
0
. Prove that there exists an index
n
n
n
for which
a
n
r
a
d
(
a
n
)
=
2022
\frac{a_n}{rad(a_n)} = 2022
r
a
d
(
a
n
)
a
n
=
2022
algebra
number theory