MathDB

Let

n

be a positive integer, and consider a sequence

a_1 , a_2 , \dotsc , a_n

of positive integers. Extend it periodically to an infinite sequence

a_1 , a_2 , \dotsc

by defining

a_{n+i} = a_i

for all

i \ge 1

. If

a_1 \le a_2 \le \dots \le a_n \le a_1 +n

and a_{a_i } \le n+i-1 \text{for} i=1,2,\dotsc, n, prove that

a_1 + \dots +a_n \le n^2.

Problem Statement