MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
IMOC Shortlist
2018-IMOC
C4
C4
Part of
2018-IMOC
Problems
(1)
set of primes is infinite
Source: IMOC 2018 C4
8/16/2021
For a sequence
{
a
i
}
i
≥
1
\{a_i\}_{i\ge1}
{
a
i
}
i
≥
1
consisting of only positive integers, prove that if for all different positive integers
i
i
i
and
j
j
j
, we have
a
i
∤
a
j
a_i\nmid a_j
a
i
∤
a
j
, then
{
p
∣
p
is a prime and
p
∣
a
i
for some
i
}
\{p\mid p\text{ is a prime and }p\mid a_i\text{ for some }i\}
{
p
∣
p
is a prime and
p
∣
a
i
for some
i
}
is a infinite set.
number theory
combinatorics