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International Contests
Tournament Of Towns
1994 Tournament Of Towns
(427) 4
(427) 4
Part of
1994 Tournament Of Towns
Problems
(1)
TOT 427 1994 Autumn A J4 subsequence from 1,1/2,1/3, ...
Source:
6/12/2024
From the sequence
1
,
1
2
,
1
3
,
.
.
.
1,\frac12, \frac13, ...
1
,
2
1
,
3
1
,
...
can one choose(a) a subsequence of
100
100
100
different numbers, (b) an infinite subsequence such that each number (beginning from the third) is equal to the difference between the two preceding numbers (
a
k
=
a
k
−
2
−
a
k
−
1
a_k=a_{k-2}-a_{k-1}
a
k
=
a
k
−
2
−
a
k
−
1
)?(SI Tokarev)
algebra
Sequence