بخش پذیری

nima1376 · 1392/6/29

نشان دهید

$127^{2}\mid 2^{126}-1$

Aria Keshtkar · 1392/6/29

پاسخ : بخش پذیری

$2^{126}-1=\left (2^{7} \right )^{18}-1=\left ( 2^{7}-1 \right )\left \left ( \sum_{i=0}^{17} \left (2^{7} \right )^{i}\right )=\left ( 2^{7}-1 \right )\left ( \left ( \sum_{i=0}^{17}\left (2^{7} \right )^{i}-1 \right )+18 \right )=\left ( 2^{7}-1 \right )\left ( \left ( 2^{7}-1 \right )\left (\sum_{i=1}^{17}\left i( 2^{7} \right )^{17-i} \right ) +18 \right )\equiv 18\left ( 2^{7}-1 \right )(mod\left (2^{7}-1 \right )^{2})$

بخش پذیری

nima1376

New Member

Aria Keshtkar

New Member