MathDB
Problems
Contests
International Contests
Junior Balkan MO
2023 Junior Balkan Mathematical Olympiad
1
1
Part of
2023 Junior Balkan Mathematical Olympiad
Problems
(1)
Classical factorial number theory
Source: JBMO 2023 Problem 1
6/26/2023
Find all pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
of positive integers such that
a
!
+
b
a!+b
a
!
+
b
and
b
!
+
a
b!+a
b
!
+
a
are both powers of
5
5
5
.Nikola Velov, North Macedonia
number theory
factorial