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Number of k-tuples is equal for odd and even k's

Source: IMO LongList 1979 - P19

June 1, 2011

number theory proposednumber theory

Problem Statement

For

k = 1, 2, \ldots

consider the

k

-tuples

(a_1, a_2, \ldots, a_k)

of positive integers such that

a_1 + 2a_2 + \cdots + ka_k = 1979.

Show that there are as many such

k

-tuples with odd

k

as there are with even

k

.

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