Explicație pas cu pas:
A=(2017+1)/2017 + (2*2017+2)/2017 +(3*2017+3)/2017 +.....+(2016*2017+2016)/2017 =>
A=1+1/2017 +2+2/2017+3+3/2017+....+2016+2016/2017 =>
A=(1+2+3+..+2016)+(1/2017+2/2017+..+2016/2017) =>
A=1008*2017+(1+2+3+...+2016)/2017 =>
A=1008*2017+1008*2017/2017 =>
A=1008*2017+1008 =>
A=1008*2018 €N (Adevarat)
1008=2⁴*3²*7
2018=2*1009
=> A=2⁵*3²*7¹*1009¹ =>
nr de divizori naturali a lui A=(5+1)(2+1)(1+1)(1+1)=72
