Question

Afla restul impartirii numarului a=1×2×3×...×2017×2018+2018 la 2017

Answer 1

   
[tex]\displaystyle\\ \frac{1\times2\times3\times \cdots\times2016\times2017\times2018+2018}{2017} = \\\\ =\frac{1\times2\times3\times \cdots\times2016\times2017\times2018}{2017} + \frac{2018}{2017}\\\ \text{Prima fractie se simplifica cu 2017 si restul este zero.}\\\\ \text{A doua fractie: } ~~ \frac{2018}{2017} = 2018 : 2017 = 1 \text{ rest } 1\\\\ \Longrightarrow~~\text{Impartirea }~~ a : 2017~~\text{are restul = 1}.[/tex]