Question

a=1+2+2la puterea a2a+2 la puterea a3a+.....+2la puterea 59. Aratati ca a este patrat perfect si cub perfect

Answer 1

$a+1=1+1+2+2^2+2^3+...+2^{59}$
$a+1=2+2+2^2+2^3+...+2^{59}$
$a+1=2^2+2^2+2^3+2^4+...+2^{59}$
$a+1=2\cdot2^2+2^3+2^4+...+2^{59}$
$a+1=2\cdot2^3+2^4+...+2^{59}$
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$a+1=2^{60}\Rightarrow a=2^{60}-1$