MathDB
Problems
Contests
International Contests
International Zhautykov Olympiad
2018 International Zhautykov Olympiad
3
3
Part of
2018 International Zhautykov Olympiad
Problems
(1)
IZHO 2018 P3 number theory
Source: izho2018
2/14/2018
Prove that there exist infinitely pairs
(
m
,
n
)
(m,n)
(
m
,
n
)
such that
m
+
n
m+n
m
+
n
divides
(
m
!
)
n
+
(
n
!
)
m
+
1
(m!)^n+(n!)^m+1
(
m
!
)
n
+
(
n
!
)
m
+
1
number theory