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Date: 20-11-2020
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Date: 9-11-2020
681
Date: 19-1-2021
1383
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Let be the th Fibonacci number, and let be a Legendre symbol so that
(1) |
A prime is called a Wall-Sun-Sun prime if
(2) |
The first few values of are 2, 3, 5, 21, 55, 39, 272, 57, ... (OEIS A113650).
There are no Wall-Sun-Sun primes up to a limit of (McIntosh 2004), subsequently extended to by PrimeGrid as of November 2015.
Let be the th Lucas number. Then
(3) |
for all primes . The first few values of are 2, 7, 0, 47, 2, 167, 287, ... (OEIS A113651).
Let be prime. Then the following are equivalent:
1. ,
2. ,
3. .
REFERENCES:
McIntosh, R. email to Paul Zimmermann. 9 Mar 2004. https://www.loria.fr/~zimmerma/records/Wieferich.status.
PrimeGrid PRPNet. "Wall-Sun-Sun Prime Search." https://prpnet.primegrid.com:13001.
Sloane, N. J. A. Sequences A113650 and A113651 in "The On-Line Encyclopedia of Integer Sequences."
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