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2023 MOAA
14
2023 MOAA Gunga P14
2023 MOAA Gunga P14
Source:
October 15, 2023
MOAA 2023
Problem Statement
Let
N
N
N
be the number of ordered triples of 3 positive integers
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
such that
6
a
6a
6
a
,
10
b
10b
10
b
, and
15
c
15c
15
c
are all perfect squares and
a
b
c
=
21
0
210
abc = 210^{210}
ab
c
=
21
0
210
. Find the number of divisors of
N
N
N
.Proposed by Andy Xu
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