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1974 Poland - Second Round
6
6
Part of
1974 Poland - Second Round
Problems
(1)
all terms of the sequence are equal.
Source: Polish MO Second Round 1974 p6
9/8/2024
There is a sequence of integers
a
1
,
a
2
,
…
,
a
2
n
+
1
a_1, a_2, \ldots, a_{2n+1}
a
1
,
a
2
,
…
,
a
2
n
+
1
with the following property: after eliminating any term, the remaining ones can be divided into two groups of
n
n
n
terms such that the sum of the terms in the first group is equal to the sum words in the second. Prove that all terms of the sequence are equal.
algebra
combinatorics