Răspuns:
a) [tex]b=\sqrt{1+3+5+...2019}=\sqrt{2020(2018:2+1):2} =\sqrt{1010*1010} =1010[/tex]∈N
b) [tex]a=\sqrt{2015n+2018}[/tex]
daca n=2k ⇒ n+1=2k+1
u(2015(2k+1)+2018)=u(5+8)=3 ⇒2015n+2018≠p² (1)
daca n=2k+1 ⇒ n+1=2k+2
u(2015(2k+2)+2018)=u(0+8)=8 ⇒2015n+2018≠p² (2)
(1), (2) ⇒ a≠p²
Explicație pas cu pas:
Patratele perfecte pot avea ca ultima cifra doar pe 0, 1, 4, 5, 6, 9.
