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2024 Argentina Cono Sur TST
Problem 6
Factorials and perfect powers
Factorials and perfect powers
Source: Argentina Cono Sur TST 2024 P6
August 9, 2024
number theory
TST
Problem Statement
Find all pairs of positive integers
(
n
,
k
)
(n, k)
(
n
,
k
)
that satisfy the equation
n
!
+
n
=
n
k
n!+n=n^k
n
!
+
n
=
n
k
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