MathDB

Infinite sequence with parallelograms

Source: Korean Summer Program Practice Test 2016 7

August 17, 2016

algebrageometryparallelogram

Problem Statement

A infinite sequence

\{ a_n \}_{n \ge 0}

of real numbers satisfy

a_n \ge n^2

. Suppose that for each

i, j \ge 0

there exist

k, l

with

(i,j) \neq (k,l)

l - k = j - i

, and

a_l - a_k = a_j - a_i

. Prove that

a_n \ge (n + 2016)^2

for some

n