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National and Regional Contests
PEN Problems
PEN H Problems
57
57
Part of
PEN H Problems
Problems
(1)
H 57
Source:
5/25/2007
Show that the equation
(
n
k
)
=
m
l
{n \choose k}=m^{l}
(
k
n
)
=
m
l
has no integral solution with
l
≥
2
l \ge 2
l
≥
2
and
4
≤
k
≤
n
−
4
4 \le k \le n-4
4
≤
k
≤
n
−
4
.
Diophantine Equations
binomial coefficients