37

Part of 2021 Saudi Arabia Training Tests

Problems(1)

max no of perfect cubes among their pairwise products

Source: 2021 Saudi Arabia Training Lists p37 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

n \ge 2

distinct positive integers

a_1, a_2, ..., a_n

none of which is a perfect cube. Find the maximal possible number of perfect cubes among their pairwise products.

perfect cubenumber theory