Ta có:
$A=5+5^2+5^3+5^4+...+5^{2019}$
$⇒$ $5A$= $5+5^2+5^3+5^4+...+5^{2019}$)
$⇒$ $5A$ = $5^2+5^3+5^4+5^5...+5^{2020}$
$⇒$ $5A-A$= $(5^2+5^3+5^4+5^5...+5^{2020})-(5+5^2+5^3+5^4+...+5^{2019})$
$⇒$ $4A$=$5^{2020}-5$
$⇒$ $4A+5$= $5^{2020}-5+5$
$⇒$ $4A+5$= $5^{2020}$
$⇒$ $4A+5$=$(5^{1005})^{2}$
$⇒$ 4A+5 là số chính phương.
$#minosuke$