Răspuns: [tex]\bf U(5^{2020}+14^{2019}+23^{2018})=8}[/tex]
Explicație pas cu pas:
(❁´◡`❁) Salutare !
[tex]\bf U(5^{2020}+14^{2019}+23^{2018})=[/tex]
[tex]\bf U(5^{2020}+4^{2019}+3^{2018})[/tex]
Un număr care are ultima cifră 5 ridicat la orice putere diferită de 0, are ultima cifră 5 ⇒ [tex]\bf U (5^{2020}) = 5[/tex]
[tex]\bf U (4^{2019})[/tex]
[tex]\bf U (4^{4k+1})=4[/tex]
[tex]\bf U (4^{4k})=6[/tex] ⇒ se repeta din 2 in 2
[tex]\bf 2019:2=1009, rest\: 1\implies \boxed{\boxed{\bf U(4^{2019})= U(4^{4k+1})=4}}[/tex]
[tex]\bf U(3^{2018})[/tex]
[tex]\bf U (3^{4k+1})=3[/tex]
[tex]\bf U (3^{4k+2})=9[/tex]
[tex]\bf U (3^{4k+3})=7[/tex]
[tex]\bf U (3^{4k})=1[/tex] ⇒ se repeta din 4 in 4
[tex]\bf 2018:4=504, rest\: 2\implies \boxed{\boxed{\bf U(3^{2018})= U(3^{4k+2})=9}}[/tex]
[tex]\boxed{\boxed{\bf U(5^{2020}+4^{2019}+3^{2018})=U(5+4+9)=U(18)=8}}[/tex]
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