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Cool problem based on smallest prime factor

Source: IMOC 2021 N2

August 11, 2021
number theorysmallest divisor

Problem Statement

Show that for any two distinct odd primes p,qp, q, there exists a positive integer nn such that {d(n),d(n+2)}={p,q}\{d(n), d(n + 2) \} = \{p, q\} where d(n)d(n) is the smallest prime factor of nn.
Proposed By - ltf0501
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