mersenneforum.org > Math Lucas-number prime factor form proofs
 Register FAQ Search Today's Posts Mark Forums Read

2012-06-08, 18:54   #1
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

3×419 Posts
Lucas-number prime factor form proofs

Quote:
 Originally Posted by Batalov Lucas1249 c262 = p115 * p147 Code: p115 = 1230907246701748850213178915950086177557919307463961418238191238338563780421891858424331033928188919064775254538919 p147 = 861662799748056902967441789531902541845512917066647559276041990818216830987090087949122773698681932527206937859817129749788517846169149201190846679 B+D
How to Prove that any prime factor for Lp ≡ 1 (mod p)
How to Prove that any prime factor for Lp ≡ 1, 9 (mod 10)

Last fiddled with by Raman on 2012-06-08 at 19:53

2012-09-12, 13:21   #2
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

125710 Posts

Quote:
 Originally Posted by Raman How to Prove that any prime factor for Lp ≡ 1 (mod p) How to Prove that any prime factor for Lp ≡ 1, 9 (mod 10)
Thus, it does so thereby, similar thing holds always for the Fibonacci numbers, candidates again with these Following examples

For this example, consider with the following statements, in the fact, in the turning process, all at once

$F_p = \begin{cases} 0\ (mod\ p) & \mbox{if } p = 5 \\ 1\ (mod\ p) & \mbox{if } p\ \equiv\ 1,\ 4\ (mod\ 5) \\ -1\ (mod\ p) & \mbox{if } p\ \equiv\ 2,\ 3\ (mod\ 5). \\ \end{cases}$

any prime factor for F[sub]p[/sup] ≡ ±1 (mod p), p ≠ 5.

On the other hand,

any prime factor for F[sub]p[/sup] ≡ 1 (mod 4), why?

i.e. all the values for F[sub]n[/sup] for all the odd values for the literal n,

are being the sum of two squares, why?,

any prime factor for 2[sub]n[/sup]-1, for odd n ≡ 1, 7 (mod 8), why?
any prime factor for 2[sub]n[/sup]+1, for odd n ≡ 1, 3 (mod 8), why?
any prime factor for 2[sub]n[/sup]+1, for even n ≡ 1, 5 (mod 8), why?

i.e. all the values for 2[sub]n[/sup]-1 for all the odd values for the literal n, aren't being the sum of two squares, why?,
i.e. all the values for 2[sub]n[/sup]+1 for all the odd values for the literal n, aren't being the sum of two squares, why?,
i.e. all the values for 2[sub]n[/sup]+1 for all the even values for the literal n, are being the sum of two squares, why?,

Last fiddled with by Raman on 2012-09-12 at 14:20

 Similar Threads Thread Thread Starter Forum Replies Last Post michael Math 31 2015-09-04 05:57 kurtulmehtap Math 21 2010-11-08 18:21 ET_ Factoring 39 2006-05-11 18:27 mpenguin Factoring 10 2005-09-29 07:46 wpolly Math 0 2004-12-01 11:14

All times are UTC. The time now is 17:17.

Sat Nov 28 17:17:46 UTC 2020 up 79 days, 14:28, 4 users, load averages: 1.77, 1.66, 1.44