I heard about this problem an year ago, but I just can't remember the name.
The problem goes like this: study the sets 



> 
> $\{a\_1,a\_2,\dotsc,a\_m\}\subseteq\mathbb{N}$ such that if $1\leq i<j\leq m$, then $a\_i a\_j+1$ is a perfect square.
> 
> 
> 


Is there a technical term for such sets?



How are such sets of natural numbers called?
Sets of $m$ integers with this property are called *integer Diophantine $m$-tuples*. A good starting point to learn about them (and about *rational* Diophantine $m$-tuples) is [this paper](https://arxiv.org/pdf/1507.00569.pdf) by 
Dujella, Kazalicki, Mikic, and Szikszai.


