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18
2014 Guts #18: Product of Factors of 30 Exceeds 900
2014 Guts #18: Product of Factors of 30 Exceeds 900
Source:
April 21, 2014
Problem Statement
Find the number of ordered quadruples of positive integers
(
a
,
b
,
c
,
d
)
(a,b,c,d)
(
a
,
b
,
c
,
d
)
such that
a
,
b
,
c
,
a,b,c,
a
,
b
,
c
,
and
d
d
d
are all (not necessarily distinct) factors of
30
30
30
and
a
b
c
d
>
900
abcd>900
ab
c
d
>
900
.
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