Let $A =$ $\{a_1, a_2, ..., a_n\}$ and $B =$ $\{b_1, b_2, ..., b_m\}$ be two sets of integers. If $a + b$ is a square for all $ a ∈ A $ and $ b ∈ B $. $A$ and $ B $ are then said to be Square Additive Sets $(SAS)$ and this is denoted by $[a_1, a_2 , ..., a_n][b_1, b_2, ..., b_m]$.
While it is possible to find $3*3$ and $4*4$ $SAS$ (here you can find some examples), I would like to know if $5*5$ $SAS$ can exist or not.