MathDB

Prefix sums of permutation

Source: Kyiv City MO 2022 Round 2, Problem 11.3

January 30, 2022

number theorypermutationsalgebra

Problem Statement

Find the largest

2022

for which there exists a permutation

k

of integers from

1

to

2022

such that for at least

k

distinct

i

with

1 \le i \le 2022

the number

\frac{a_1 + a_2 + \ldots + a_i}{1 + 2 + \ldots + i}

is an integer larger than

1

.
(Proposed by Oleksii Masalitin)

Back to Problems View on AoPS