Răspuns:
2S = 2016×2017×2018
Explicație pas cu pas:
x = 2017×c + r, c = r, 0 ≤ r < 2017 => 0 ≤ c < 2017
<=> 0 ≤ c ≤ 2016
x = 2017×c + c = 2018×c
notăm cu S suma numerelor:
[tex]S = 2018 \cdot 0 + 2018 \cdot 1 + ... + 2018 \cdot 2016 = \\ = 2018 \cdot (1 + 2 + ... + 2016)[/tex]
[tex]2S = 2 \cdot 2018 \cdot (1 + 2 + ... + 2016) = \\ = 2 \cdot 2018 \cdot \frac{2016 \cdot 2017}{2} = \red{\bf 2016 \cdot 2017 \cdot 2018}[/tex]
q.e.d.
