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a_i a_j, a_i+a_j , |a_i -a_j |, i \ne j, max no distinct odd integers

Source: 2002 Estonia National Olympiad Final Round grade 10 p3

March 16, 2020

number theoryoddSumProduct

Problem Statement

John takes seven positive integers

a_1,a_2,...,a_7

and writes the numbers

a_i a_j

a_i+a_j

and

|a_i -a_j |

for all

i \ne j

on the blackboard. Find the greatest possible number of distinct odd integers on the blackboard.