For $i\in\{1,2\}$ let $A_i$ be a commutative ring with unity whose additive group is free and finitely-generated. Assume that $A_i$ is connected in the sense that $0$ and $1$ are unique solutions of the equation $x^2=x$ in $A_i$. Denote by $\mu(A_i)$ the group of roots of unity of $A_i$, i.e., the elements of finite multiplicative order in $A_i$.

>**Problem.** Is the map $$\mu(A_1)\times\mu(A_2)\ \longrightarrow\ \mu(A_1\otimes_{\mathbb Z}A_2),\;\;(u,v)\ \longmapsto\ u\otimes v,$$
surjective?

(The problem is posed 9.07.2018 by Tristan Tilly from Leiden University on page 25 of [Volume 2][1] of the [Lviv Scottish Book][2]). 
  
**Prize for solution:** An eternal welcome in Netherlands, and a bottle of liquor of your choice.

  [1]: http://www.math.lviv.ua/szkocka/viewbook.php?vol=2
  [2]: http://www.math.lviv.ua/szkocka