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IMO Longlists
1979 IMO Longlists
19
19
Part of
1979 IMO Longlists
Problems
(1)
Number of k-tuples is equal for odd and even k's
Source: IMO LongList 1979 - P19
6/1/2011
For
k
=
1
,
2
,
…
k = 1, 2, \ldots
k
=
1
,
2
,
…
consider the
k
k
k
-tuples
(
a
1
,
a
2
,
…
,
a
k
)
(a_1, a_2, \ldots, a_k)
(
a
1
,
a
2
,
…
,
a
k
)
of positive integers such that
a
1
+
2
a
2
+
⋯
+
k
a
k
=
1979.
a_1 + 2a_2 + \cdots + ka_k = 1979.
a
1
+
2
a
2
+
⋯
+
k
a
k
=
1979.
Show that there are as many such
k
k
k
-tuples with odd
k
k
k
as there are with even
k
k
k
.
number theory proposed
number theory