Question Number 84553 by naka3546 last updated on 14/Mar/20
$${Find}\:\:{mininum}\:\:{value}\:\:{of}\:\:{n}\:\:{such}\:\:{that} \\ $$$${both}\:\:{n}\:+\:\mathrm{3}\:\:\:{and}\:\:\mathrm{2020}{n}\:+\:\mathrm{1}\:\:{are}\:\:{square}\:\:{numbers}\:. \\ $$
Commented by mr W last updated on 14/Mar/20
$${i}\:{got}\:{n}_{{min}} =\mathrm{2022} \\ $$$$\mathrm{2022}+\mathrm{3}=\mathrm{2025}=\mathrm{45}^{\mathrm{2}} \:\Rightarrow{ok} \\ $$$$\mathrm{2020}×\mathrm{2022}+\mathrm{1}=\left(\mathrm{2021}−\mathrm{1}\right)\left(\mathrm{2021}+\mathrm{1}\right)+\mathrm{1}=\mathrm{2021}^{\mathrm{2}} \:\Rightarrow{ok} \\ $$
Commented by naka3546 last updated on 14/Mar/20
$${how}\:\:{about}\:\:{n}\:=\:\mathrm{726}\:? \\ $$
Commented by mr W last updated on 14/Mar/20
$${yes}.\:\mathrm{726}\:{is}\:{the}\:{smallest}\:{n}. \\ $$