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2022 JBMO Shortlist
N1
JBMO Shortlist 2022 N1
JBMO Shortlist 2022 N1
Source: JBMO Shortlist 2022
June 26, 2023
number theory
factorial
sum of integers
Junior
Balkan
shortlist
Problem Statement
Determine all pairs
(
k
,
n
)
(k, n)
(
k
,
n
)
of positive integers that satisfy
1
!
+
2
!
+
.
.
.
+
k
!
=
1
+
2
+
.
.
.
+
n
.
1! + 2! + ... + k! = 1 + 2 + ... + n.
1
!
+
2
!
+
...
+
k
!
=
1
+
2
+
...
+
n
.
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