Răspuns:
a) nu
b) nu
Explicație pas cu pas:
U(x)∈{0,1,2,3,4,5,6,7,8,9}
U(x^4)∈{0,1,5,6}; deci si U(y^4)∈{0,1,5,6}; ⇒U(x^4 + y^4)∈{0,1,2,5,6,7}
U(2019²⁰²⁰)=U(9²⁰²⁰)=U(9²)=1, ⇒U(2019²⁰²⁰+3)=U(1+3)=4
Deoarece 4∉{0,1,2,5,6,7}, ⇒nu exista...
b) U(x^4 + y^4)∈{0,1,2,5,6,7}; U(z^4)∈{0,1,5,6}; ⇒
U(x^4 + y^4 + z^4)∈{0,1,2,3,5,6,7,8}
Deoarece 4∉{0,1,2,3,5,6,7,8}, ⇒nu exista...
