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Old 2012-06-08, 18:54   #1
Raman
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Default Lucas-number prime factor form proofs

Quote:
Originally Posted by Batalov View Post
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
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Old 2012-09-12, 13:21   #2
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Quote:
Originally Posted by Raman View Post
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
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