Răspuns: [tex]\large \red{\bf \overline{abc}=327}[/tex]
Explicație pas cu pas:
Fie [tex]\large \bf \overline{abc}[/tex] - numerele de trei cifre căutate
[tex]\large \bf a, b, c~- cifre[/tex]
[tex]\large \bf a, b, c~ \in ~ \big\{0,1,2,3,4,5,6,7,8,9\big\}[/tex]
[tex]\large \bf a\neq 0, ~deoarece ~un ~numar ~nu~ poate~ incepe~ cu~ 0[/tex]
[tex]\large \bf a^{a} = \overline{bc} \in \Big\{1^{1},2^{2},3^{3},4^{4},5^{5},6^{6},7^{7},8^{8},9^{9}\Big\}[/tex]
[tex]\large \bf a^{a} = 1^{1} = 1 ~nu ~convine[/tex]
[tex]\large \bf a^{a} = 2^{2} = 4 ~nu ~convine[/tex]
[tex]\large \bf \red{a^{a} = 3^{3} = 27 \implies solutie}[/tex]
[tex]\large \bf a^{a} = 4^{4} = 256 ~~Nu ~convine, deoarece ~e~nr ~mai~ mare~ de~ 2~ cifre[/tex]
[tex]\large \bf a^{a} = 5^{5} = 3125~~Nu ~convine, deoarece ~e~nr ~mai~ mare~ de~ 2~ cifre[/tex]
[tex]\large \bf .~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~[/tex]
[tex]\large \bf a = 3[/tex]
[tex]\large \bf \overline{bc} = 27 \implies \red{\boxed{\bf \overline{abc}=327}}[/tex]
Bafta multa !
