[tex]\displaystyle\it\\\overline{abc}=b^b-b-c,~a,b,c~cifre.\\evident,~100\leq \overline{abc}\leq 999 \implies 100\leq b^b-b-c\leq 999 \implies b\leq 4.\\daca~b\leq 3 \implies b^b-b-c\leq 100,~deci~evident~\boxed{\it b=4}~.\\\overline{abc}=b^b-b-c \Leftrightarrow 100a+10b+c=b^b-b-c \Leftrightarrow 100a+2c=b^b-b-10b,~\\dar~b=4 \implies 100a+2c=4^4-4-40=212,~impartim~membrii~ecuatiei~la~2.\\50a+c=106,~evident~a~va~fi~2,~atlfel~50a+c\leq 100.\\100+c=106 \implies c=6.\\asadar,~\boxed{\it \overline{abc}=246}~.[/tex]
