MathDB
Problems
Contests
International Contests
IMO Shortlist
2015 IMO Shortlist
N2
N2
Part of
2015 IMO Shortlist
Problems
(1)
Factorials divide
Source: 2015 ISL N2
7/7/2016
Let
a
a
a
and
b
b
b
be positive integers such that
a
!
+
b
!
a! + b!
a
!
+
b
!
divides
a
!
b
!
a!b!
a
!
b
!
. Prove that
3
a
≥
2
b
+
2
3a \ge 2b + 2
3
a
≥
2
b
+
2
.
factorial
number theory
IMO Shortlist
Divisibility