MathDB
Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2019 India PRMO
18
18
Part of
2019 India PRMO
Problems
(2)
Combinatorics / Multinomial
Source:
8/11/2019
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
?
Multinomial Theorem
combinatorics
Factors Of A Prime
Source: PRMO Leg 2 P18
8/25/2019
What is the smallest prime number
p
p
p
such that
p
3
+
4
p
2
+
4
p
p^3+4p^2+4p
p
3
+
4
p
2
+
4
p
has exactly
30
30
30
positive divisors ?