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Divisibility example.

If $$d|n$$ then prove that $${ 2 }^{ d }-1|{ 2 }^{ n }-1$$.

This is my solution

If $$d|n$$ then $$n=dk$$ for some $$k$$.Then we have to prove $${ 2 }^{ d }-1|{ 2 }^{ dn }-1$$ or $${ 2 }^{ d }-1|{ ({ 2 }^{ d }) }^{ k }-1$$.Now let $$x={ 2 }^{ d }$$ therefore we have to prove $$x-1|{ x }^{ k }-1$$ which is true by Remainder theorem.

Note by Shivamani Patil
2 years, 7 months ago

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NICE but too EASY. · 2 years, 7 months ago

Math is neither easy nor difficult for her lover.@Krishna Ar · 2 years, 7 months ago

haha · 2 years, 7 months ago

Your proof is awesome. · 2 years, 7 months ago

Thanx.@Adarsh Kumar · 2 years, 7 months ago