If $$ 2^{96}-1 $$ is divisible by two integers between 60 and 70, what are the two numbers?

Question

Uniteasy Admin · Accepted Answer

$$ 2^{96}-1 $$
$$ =(2^{48}+1)(2^{48}-1) $$
$$ = (2^{48}+1)(2^{24}+1)(2^{24}-1) $$
$$ = (2^{48}+1)(2^{24}+1)(2^{12}+1)(2^{12}-1) $$
$$ = (2^{48}+1)(2^{24}+1)(2^{12}+1)(2^6+1)(2^6-1) $$
$$ = (2^{48}+1)(2^{24}+1)(2^{12}+1) × 65×63 $$

Question

Answer