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Kvant 2022
M2716
M2716
Part of
Kvant 2022
Problems
(1)
Product divisible with factorial
Source: Kvant Magazine No. 9 2022 M2716
3/8/2023
Find all pairs of natural numbers
(
k
,
m
)
(k, m)
(
k
,
m
)
such that for any natural
n
n{}
n
the product
(
n
+
m
)
(
n
+
2
m
)
⋯
(
n
+
k
m
)
(n+m)(n+2m)\cdots(n+km)
(
n
+
m
)
(
n
+
2
m
)
⋯
(
n
+
km
)
is divisible by
k
!
k!{}
k
!
.Proposed by P. Kozhevnikov
Kvant
number theory
factorial