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Old 2002-11-21, 10:54   #5
TTn
 

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Well, Fibonacci numbers are smaller than the currently used Lehmer test numbers, but the algorithm lay undiscovered.

For example Lucas sequence 2,1, 3 ,4, 7 ,11,18,29...
L(2^n) =
3, then 3^2 -2 =7, then 7^2-2=47, and so on, just like Lehmer test but with a smaller starting number of three.



I found more !


Let p be a prime>7 satisfying the following conditions:
1. p= 2,4(mod 5)
2. 2^[p+1] -3, is also prime
Then (2^[p+1]-3) | F(2^p-1)

Let p be a prime>5 satisfying the following conditions:
1. p = 4 (mod5)
2. 2^[p+1]-1 is also prime
Then(2^[p+1]-1) | L(2^p-1)



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