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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
3 years ago

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NICE but too EASY.

Krishna Ar - 3 years ago

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Math is neither easy nor difficult for her lover.@Krishna Ar

Shivamani Patil - 3 years ago

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haha

Krishna Ar - 3 years ago

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Your proof is awesome.

Adarsh Kumar - 3 years ago

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Thanx.@Adarsh Kumar

Shivamani Patil - 3 years ago

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nice....

Vivek Waghmare - 3 years ago

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