MathDB
Problems
Contests
National and Regional Contests
Germany Contests
Germany Team Selection Test
2018 Germany Team Selection Test
2018 Germany Team Selection Test
Part of
Germany Team Selection Test
Subcontests
(1)
2
1
Hide problems
Permutation of Positive Integers with Bounded Difference
A positive integer
d
d
d
and a permutation of positive integers
a
1
,
a
2
,
a
3
,
…
a_1,a_2,a_3,\dots
a
1
,
a
2
,
a
3
,
…
is given such that for all indices
i
≥
1
0
100
i\geq 10^{100}
i
≥
1
0
100
,
∣
a
i
+
1
−
a
i
∣
≤
2
d
|a_{i+1}-a_{i}|\leq 2d
∣
a
i
+
1
−
a
i
∣
≤
2
d
holds. Prove that there exists infinity many indices
j
j
j
such that
∣
a
j
−
j
∣
<
d
|a_j -j|< d
∣
a
j
−
j
∣
<
d
.