MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2018 Latvia Baltic Way TST
P14
P14
Part of
2018 Latvia Baltic Way TST
Problems
(1)
Sequence of biggest prime divisors
Source: 2018 Latvia BW TST P14
3/26/2022
Let
a
1
,
a
2
,
.
.
.
a_1,a_2,...
a
1
,
a
2
,
...
be a sequence of positive integers with
a
1
=
2
a_1=2
a
1
=
2
. For each
n
≥
1
n \ge 1
n
≥
1
,
a
n
+
1
a_{n+1}
a
n
+
1
is the biggest prime divisor of
a
1
a
2
.
.
.
a
n
+
1
a_1a_2...a_n+1
a
1
a
2
...
a
n
+
1
. Prove that the sequence does not contain numbers
5
5
5
and
11
11
11
.
number theory
number theory unsolved
Integer sequence