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National and Regional Contests
Serbia Contests
Serbia Team Selection Test
1998 Yugoslav Team Selection Test
Problem 3
Problem 3
Part of
1998 Yugoslav Team Selection Test
Problems
(1)
arith. seq: nCk, nC(k+1), nC(k+2), nC(k+3)
Source: Yugoslav TST 1998 P3
5/15/2021
Prove that there are no positive integers
n
n
n
and
k
≤
n
k\le n
k
≤
n
such that the numbers
(
n
k
)
,
(
n
k
+
1
)
,
(
n
k
+
2
)
,
(
n
k
+
3
)
\binom nk,\binom n{k+1},\binom n{k+2},\binom n{k+3}
(
k
n
)
,
(
k
+
1
n
)
,
(
k
+
2
n
)
,
(
k
+
3
n
)
in this order form an arithmetic progression.
algebra
Sequence