MathDB
Problems
Contests
International Contests
JBMO ShortLists
2021 JBMO Shortlist
N1
N1
Part of
2021 JBMO Shortlist
Problems
(1)
JBMO Shortlist 2021 N1
Source: JBMO Shortlist 2021
7/2/2022
Find all positive integers
a
,
b
,
c
a, b, c
a
,
b
,
c
such that
a
b
+
1
ab + 1
ab
+
1
,
b
c
+
1
bc + 1
b
c
+
1
, and
c
a
+
1
ca + 1
c
a
+
1
are all equal to factorials of some positive integers.Proposed by Nikola Velov, Macedonia
Junior
Balkan
shortlist
2021
number theory
factorial