MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
49
49
Part of
PEN A Problems
Problems
(1)
A 49
Source:
5/25/2007
Prove that there is no positive integer
n
n
n
such that, for
k
=
1
,
2
,
⋯
,
9
,
k=1, 2, \cdots, 9,
k
=
1
,
2
,
⋯
,
9
,
the leftmost digit of
(
n
+
k
)
!
(n+k)!
(
n
+
k
)!
equals
k
k
k
.
inequalities
Divisibility Theory