MathDB

min a_{2010}, a_n < a_{n+1}, a_i + a_l > a_j + a_k

Source: 2010 Dutch IMO TST2 p1

January 10, 2020

minimumalgebraSequence

Problem Statement

Consider sequences

a_1, a_2, a_3,...

of positive integers. Determine the smallest possible value of

a_{2010}

if (i)

a_n < a_{n+1}

for all

n\ge 1

, (ii)

a_i + a_l > a_j + a_k

for all quadruples

(i, j, k, l)

which satisfy

1 \le i < j \le k < l