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Ireland National Math Olympiad
2019 Irish Math Olympiad
1
1
Part of
2019 Irish Math Olympiad
Problems
(1)
is 1000 a quasi-prime ?
Source: 2019 Irish Mathematical Olympiad paper 1 p1
10/5/2020
De fine the quasi-primes as follows.
∙
\bullet
∙
The first quasi-prime is
q
1
=
2
q_1 = 2
q
1
=
2
∙
\bullet
∙
For
n
≥
2
n \ge 2
n
≥
2
, the
n
t
h
n^{th}
n
t
h
quasi-prime
q
n
q_n
q
n
is the smallest integer greater than
q
n
1
q_{n_1}
q
n
1
and not of the form
q
i
q
j
q_iq_j
q
i
q
j
for some
1
≤
i
≤
j
≤
n
−
1
1 \le i \le j \le n - 1
1
≤
i
≤
j
≤
n
−
1
. Determine, with proof, whether or not
1000
1000
1000
is a quasi-prime.
number theory