2 (1+2+3+....+2019)+ 2020
folosim suma lui Gauss pentru (1+2+3+....+2019):
S= 2019(2019+1)/2
S= (2019•2020)/2
S= 4078380/2
S= 2039190
o reintroducem in numar:
2 (2039190)+ 2020
4078380+ 2020
4080400 (numărul)
√4080400= 2020 (deci numărul este pătrat perfect, 2020²= 4080400)
2×(1+2+3+...+2019)+2020=
=2×2019×2020÷2+2020=
=2019×2020+2020=
=2019×2020+1×2020=
=2020×(2019+1)=
=2020×2020=
=2020² ⇒ este pătrat perfect