Alice wrote a sequence of $n > 2$ nonzero nonequal numbers such that each is greater than the previous one by the same amount. Bob wrote the inverses of those n numbers in some order. It so happened that each number in his row also is greater than the previous one by the same amount, possibly not the same as in Alice’s sequence. What are the possible values of $n{}$? Alexey Zaslavsky
Problem
Source: 43rd International Tournament of Towns, Junior A-Level P1, Fall 2021
Tags: combinatorics, algebra, Tournament of Towns