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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
29
29
Part of
PEN A Problems
Problems
(1)
A 29
Source:
5/25/2007
For which positive integers
k
k
k
, is it true that there are infinitely many pairs of positive integers
(
m
,
n
)
(m, n)
(
m
,
n
)
such that
(
m
+
n
−
k
)
!
m
!
n
!
\frac{(m+n-k)!}{m! \; n!}
m
!
n
!
(
m
+
n
−
k
)!
is an integer?
Divisibility Theory