 ×     #### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

if 2^n+1 is prime then prove that n isa power of 2


6 years ago IIT Delhi
174 Points If $n$is a positive integer but not a power of 2, then $n = rs$where $1 \le r < n$, $1 < s \le n$and $s$is odd.By the preceding lemma, for positive integer $m$, $(a-b) \mid (a^m-b^m)$where $\mid$means "evenly divides". Substituting $a = 2^r$, $b = -1$, and $m = s$and using that $s$is odd, $(2^r+1) \mid (2^{rs}+1),$and thus $(2^r+1) \mid (2^n+1).$Because $1 < 2^r+1 < 2^n+1$, it follows that $2^n+1$is not prime. Therefore, by contraption $n$must be a power of 2.sher mohammadb.tech, iit delhi

6 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »  ### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions