Factor of a Mersenne number – math.stackexchange.com

Why is it true that if 7 divides 91 then $(2^7-1) $ divides $(2^{91}-1)$? 1) $2^{91}-1$ $7|91 \implies (2^7-1)|(2^{91}-1)$ $\implies 2^7-1$ is factor 2) $2^{1001}-1$ $7|1001 \implies ...

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