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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, 5 months ago

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NICE but too EASY. Krishna Ar · 2 years, 5 months ago

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@Krishna Ar Math is neither easy nor difficult for her lover.@Krishna Ar Shivamani Patil · 2 years, 5 months ago

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@Shivamani Patil haha Krishna Ar · 2 years, 5 months ago

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Your proof is awesome. Adarsh Kumar · 2 years, 5 months ago

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@Adarsh Kumar Thanx.@Adarsh Kumar Shivamani Patil · 2 years, 5 months ago

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@Adarsh Kumar nice.... Vivek Waghmare · 2 years, 5 months ago

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