Question

Give an example of a set A = {1,2,...,k} for a smallest k in N having subsets A1 , A2, A3 such that /Ai - Aj/ = /Aj - Ai/ = /i-j/ for every two integers i and j with (1 less or equal to i less j less or equal to 3).

Answer 1

for every two integers i and j with 1 \[\le i < j \le 3\]