a) a= 2019+2•(1+2+3+...+2018)
[tex]a = 2019 + 2 \times \frac{2018 \times 2019}{2} [/tex]
[tex]a = 2019 + 2018 \times 2019[/tex]
[tex]a = 2019 \times (1 + 2018) [/tex]
a=2019•2019
a=2019²=> a= pătrat perfect
b)
[tex] \frac{ {a}^{2} - a }{2018} = \frac{a(a - 1)}{2018} = \frac{2019(2019 - 1)}{2018} = [/tex]
[tex] = \frac{2018 \times 2019}{2018} = > [/tex]
fractia e divizibila cu 2018, deci restul este 0.
