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Kürschák Math Competition
1973 Kurschak Competition
1
1
Part of
1973 Kurschak Competition
Problems
(1)
binomials in arithmetic progression
Source: 1973 Hungary - Kürschák Competition p1
10/15/2022
For what positive integers
n
,
k
n, k
n
,
k
(with
k
<
n
k < n
k
<
n
) are the binomial coefficients
(
n
k
−
1
)
,
(
n
k
)
,
(
n
k
+
1
)
{n \choose k- 1} \,\,\, , \,\,\, {n \choose k} \,\,\, , \,\,\, {n \choose k + 1}
(
k
−
1
n
)
,
(
k
n
)
,
(
k
+
1
n
)
three successive terms of an arithmetic progression?
binomial coefficients
Combinations
algebra
arithmetic sequence