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Poland - Second Round
1978 Poland - Second Round
3
3
Part of
1978 Poland - Second Round
Problems
(1)
choose from sequence, a finite sequence with sum of terms = k
Source: Polish MO Recond Round 1978 p3
9/9/2024
Given a sequence of natural numbers
(
a
i
)
(a_i)
(
a
i
)
, for each natural number
n
n
n
the sum of the terms of the sequence that are not greater than
n
n
n
is a number not less than
n
n
n
. Prove that for every natural number
k
k
k
it is possible to choose from the sequence
(
a
i
)
(a_i)
(
a
i
)
a finite sequence with the sum of terms equal to
k
k
k
.
algebra
number theory