Question

repede va dau coroana!!!​

Answer 1

Răspuns: $\bf U(5^{2020}+14^{2019}+23^{2018})=8}$

Explicație pas cu pas:

(❁´◡`❁)  Salutare !        

$\bf U(5^{2020}+14^{2019}+23^{2018})=$

$\bf U(5^{2020}+4^{2019}+3^{2018})$

Un număr care are ultima cifră 5 ridicat la orice putere diferită de 0, are ultima cifră 5 ⇒ $\bf U (5^{2020}) = 5$        

$\bf U (4^{2019})$

$\bf U (4^{4k+1})=4$

$\bf U (4^{4k})=6$     ⇒  se repeta din 2 in 2

$\bf 2019:2=1009, rest\: 1\implies \boxed{\boxed{\bf U(4^{2019})= U(4^{4k+1})=4}}$

$\bf U(3^{2018})$

$\bf U (3^{4k+1})=3$

$\bf U (3^{4k+2})=9$

$\bf U (3^{4k+3})=7$

$\bf U (3^{4k})=1$         ⇒  se repeta din 4 in 4

$\bf 2018:4=504, rest\: 2\implies \boxed{\boxed{\bf U(3^{2018})= U(3^{4k+2})=9}}$

                             

$\boxed{\boxed{\bf U(5^{2020}+4^{2019}+3^{2018})=U(5+4+9)=U(18)=8}}$

==pav38==