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India Pre-Regional Mathematical Olympiad
2019 India PRMO
18
Combinatorics / Multinomial
Combinatorics / Multinomial
Source:
August 11, 2019
Multinomial Theorem
combinatorics
Problem Statement
Find the number of ordered triples
(
a
,
b
)
(a, b)
(
a
,
b
)
of positive integers with
a
<
b
a < b
a
<
b
and
100
≤
a
,
b
≤
1000
100 \leq a, b \leq 1000
100
≤
a
,
b
≤
1000
satisfy
gcd
(
a
,
b
)
:
l
c
m
(
a
,
b
)
=
1
:
495
\gcd(a, b) : \mathrm{lcm}(a, b) = 1 : 495
g
cd
(
a
,
b
)
:
lcm
(
a
,
b
)
=
1
:
495
?
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