|

Algebra

Hot goIITian

 Joined: 10 Oct 2011 Post: 120
29 Mar 2012 10:38:59 IST
2 People liked this
5
287
dout
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

Do any odd perfect numbers exist?

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
29 Mar 2012 11:37:13 IST
1 people liked this

No odd perfect numbers is found till now .But there are no proofs stating the non existence of perfect numbers. Many great mathematicians said they won't exist. I have read somewhere that with the help of high performance supercomputers the perfect numbers were calculated upto very large numbers and weren't found odd. But nobody rules out the probability of finding an odd perfect number

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
29 Mar 2012 12:12:43 IST
1 people liked this

This Might help u machan ......

## Odd perfect numbers

 Are there any odd perfect numbers?

It is unknown whether there are any odd perfect numbers, though various results have been obtained. Carl Pomerance has presented a heuristic argument which suggests that no odd perfect numbers exist. All perfect numbers are also Ore's harmonic numbers, and it has been conjectured as well that there are no odd Ore's harmonic numbers other than 1.

Any odd perfect number N must satisfy the following conditions:

• N > 101500, result published in 2012.
• N is of the form
$N=q^{\alpha} p_1^{2e_1} \cdots p_k^{2e_k},$
where:
• qp1, ..., pk are distinct primes (Euler).
• q ≡ α ≡ 1 (mod 4) (Euler).
• The smallest prime factor of N is less than (2k + 8) / 3.
• Either qα > 1062, or p j2ej  > 1062 for some j.
• N < 24k+1.[11]
• The largest prime factor of N is greater than 108.
• The second largest prime factor is greater than 104, and the third largest prime factor is greater than 100.[13][14]
• N has at least 101 prime factors and at least 9 distinct prime factors. If 3 is not one of the factors of N, then N has at least 12 distinct prime factors.

In 1888, Sylvester stated:

...a prolonged meditation on the subject has satisfied me that the existence of any one such [odd perfect number] — its escape, so to say, from the complex web of conditions which hem it in on all sides — would be little short of a miracle.

Hot goIITian

Joined: 10 Oct 2011
Posts: 120
29 Mar 2012 13:26:44 IST
0 people liked this

thank you both of you :)  i was thinking about it for long time :) great information sathyaram macha  :) i thought only  6 millinieum problems are unsolved in mathematics :)

Hot goIITian

Joined: 10 Oct 2011
Posts: 120
29 Mar 2012 13:29:30 IST
0 people liked this

another question - how to rate people ? i dont understnad it

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
29 Mar 2012 13:38:36 IST
0 people liked this

rate is nthin but to like it da machan..... For Ex.Just click Like for this comment...That is rate...HAhahah lolz :P

 Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a avatar to have your pictures show up by your comment If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

## For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 10080 m Post - 2213
4. edison
 Altitude - 10825 m Post - 7804
5. Sagar Saxena
 Altitude - 8635 m Post - 8064
 Altitude - 6330 m Post - 1958

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone