Divisibility

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mathlover007
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Joined: Sun Dec 10, 2017 5:14 pm

Divisibility

Unread post by mathlover007 » Fri Dec 15, 2017 9:36 pm

Find n such that 2n31024 − 1.

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samiul_samin
Posts: 999
Joined: Sat Dec 09, 2017 1:32 pm

Re: Divisibility

Unread post by samiul_samin » Thu Mar 01, 2018 7:38 pm

mathlover007 wrote:
Fri Dec 15, 2017 9:36 pm
Find n such that 2n31024 − 1.
The correct question is,
Find the highest value of $n$ such that $2^n|3^{1024}-1$.
Hint
$2^{10}=1024$
$3^{2k}+1$ is divided by $2$.
Use the formula $x^2-y^2=(x+y)(x-y)$
Answer
$9+2+1=12$

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