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.

## Comments

Sort by:

TopNewestNICE but too EASY. – Krishna Ar · 2 years, 1 month ago

Log in to reply

@Krishna Ar – Shivamani Patil · 2 years, 1 month ago

Math is neither easy nor difficult for her lover.Log in to reply

– Krishna Ar · 2 years, 1 month ago

hahaLog in to reply

Your proof is awesome. – Adarsh Kumar · 2 years, 1 month ago

Log in to reply

@Adarsh Kumar – Shivamani Patil · 2 years, 1 month ago

Thanx.Log in to reply

– Vivek Waghmare · 2 years, 1 month ago

nice....Log in to reply