MathDB
Problems
Contests
International Contests
Middle European Mathematical Olympiad
2015 Middle European Mathematical Olympiad
7
7
Part of
2015 Middle European Mathematical Olympiad
Problems
(1)
Factorial and exponential diophantine equation
Source: MEMO 2015, problem T-7
8/28/2015
Find all pairs of positive integers
(
a
,
b
)
(a,b)
(
a
,
b
)
such that
a
!
+
b
!
=
a
b
+
b
a
.
a!+b!=a^b + b^a.
a
!
+
b
!
=
a
b
+
b
a
.
factorial
Diophantine equation
number theory
Exponential equation