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(1)
Cool problem based on smallest prime factor
Source: IMOC 2021 N2
8/11/2021
Show that for any two distinct odd primes
p
,
q
p, q
p
,
q
, there exists a positive integer
n
n
n
such that
{
d
(
n
)
,
d
(
n
+
2
)
}
=
{
p
,
q
}
\{d(n), d(n + 2) \} = \{p, q\}
{
d
(
n
)
,
d
(
n
+
2
)}
=
{
p
,
q
}
where
d
(
n
)
d(n)
d
(
n
)
is the smallest prime factor of
n
n
n
.Proposed By - ltf0501
number theory
smallest divisor