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National and Regional Contests
Iran Contests
Iran Team Selection Test
2024 Iran Team Selection Test
10
10
Part of
2024 Iran Team Selection Test
Problems
(1)
Another infinite prime divisors problem
Source: Iran Team selection test 2024 - P10
5/19/2024
Let
{
a
n
}
\{a_n\}
{
a
n
}
be a sequence of natural numbers such that each prime number greater than
1402
1402
1402
divides a member of that. Prove that the set of prime divisors of members of sequence
{
b
n
}
\{b_n\}
{
b
n
}
which
b
n
=
a
1
a
2
.
.
.
a
n
−
1
b_n=a_1a_2...a_n-1
b
n
=
a
1
a
2
...
a
n
−
1
, is infinite.Proposed by Navid Safaei
number theory