Предмет: Алгебра, автор: Mitek007

Доказать, что (8 в степени 7 минус 2 в степени 15) делится на 7

Ответы

Автор ответа: Vinn

$8^7 - 2^{15} = (2^3)^7 - 2^{15} = 2^{21} - 2^{15} =$

$= 2^{15}(2^6 - 1) = 2^{15}(64-1) = 2^{15}cdot63$

А 63 делится на 7. Значит 8^7 - 2^15 тоже делится на 7.

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