The notion of the radical occurs in the abc conjecture, which states that, for any ε > 0 {\displaystyle \varepsilon >0} , there exists a finite K ε {\displaystyle K_{\varepsilon }} such that, for all triples of coprime positive integers a {\displaystyle a} , b {\displaystyle b} , and c {\displaystyle c} satisfying a + b = c {\displaystyle a+b=c} ,[1]