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Cono Sur Olympiad
2023 Cono Sur Olympiad
1
1
Part of
2023 Cono Sur Olympiad
Problems
(1)
Sum of powers of integers less or equal 2023
Source: Cono Sur 2023 #1
8/7/2023
A list of
n
n
n
positive integers
a
1
,
a
2
,
a
3
,
…
,
a
n
a_1, a_2,a_3,\ldots,a_n
a
1
,
a
2
,
a
3
,
…
,
a
n
is said to be good if it checks simultaneously:
∙
a
1
<
a
2
<
a
3
<
⋯
<
a
n
,
\bullet a_1<a_2<a_3<\cdots<a_n,
∙
a
1
<
a
2
<
a
3
<
⋯
<
a
n
,
∙
a
1
+
a
2
2
+
a
3
3
+
⋯
+
a
n
n
≤
2023.
\bullet a_1+a_2^2+a_3^3+\cdots+a_n^n\le 2023.
∙
a
1
+
a
2
2
+
a
3
3
+
⋯
+
a
n
n
≤
2023.
For each
n
≥
1
n\ge 1
n
≥
1
, determine how many good lists of
n
n
n
numbers exist.
inequalities
Sum of powers
cono sur