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2018 International Zhautykov Olympiad
3
IZHO 2018 P3 number theory
IZHO 2018 P3 number theory
Source: izho2018
February 14, 2018
number theory
Problem Statement
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
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