OFFSET
1,1
COMMENTS
From Jianing Song, Oct 13 2022: (Start)
Rational primes that decompose in the field Q(sqrt(30)).
Primes p such that kronecker(30,p) = 1 (or equivalently, kronecker(120,p) = 1).
Primes congruent to 1, 7, 13, 17, 19, 29, 37, 49, 71, 83, 91, 101, 103, 107, 113, 119 modulo 120. (End)
LINKS
EXAMPLE
7 is a term since it is a prime and 6^((7-1)/2) - 5^((7-1)/2) = 6^3 - 5^3 = 91 = 7*13 is divisible by 7.
MATHEMATICA
Select[Prime[Range[200]], Divisible[6^((#-1)/2)-5^((#-1)/2), #]&] (* Harvey P. Dale, Jun 06 2018 *)
Select[Range[3, 600, 2], PrimeQ[#] && PowerMod[5, (# - 1)/2, #] == PowerMod[6, (# - 1)/2, #] &] (* Amiram Eldar, Apr 07 2021 *)
PROG
(PARI) \\ s = +-1, d=diff
ptopm1d2(n, x, d, s) = { forprime(p=3, n, p2=(p-1)/2; y=x^p2 + s*(x-d)^p2; if(y%p==0, print1(p", "))) }
ptopm1d2(1000, 6, 1, -1)
(PARI) isA097959(p) == isprime(p) && kronecker(30, p) == 1 \\ Jianing Song, Oct 13 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Sep 06 2004
EXTENSIONS
Definition clarified by Harvey P. Dale, Jun 06 2018
STATUS
approved