A097956 Primes p such that p divides 5^(p-1)/2 - 3^(p-1)/2.

7, 11, 17, 43, 53, 59, 61, 67, 71, 103, 109, 113, 127, 131, 137, 163, 173, 179, 181, 191, 197, 223, 229, 233, 239, 241, 251, 257, 283, 293, 307, 311, 317, 349, 353, 359, 367, 409, 419, 421, 431, 463, 479, 487, 491, 523, 541, 547, 557, 593, 599, 601, 607, 617

Offset: 1

Author

Cino Hilliard, Sep 06 2004

Keywords

• nonn
• easy

Comments

From Jianing Song, Oct 13 2022: (Start)

Rational primes that decompose in the field Q(sqrt(15)).

Primes p such that kronecker(60,p) = 1.

Primes congruent to 1, 7, 11, 17, 43, 49, 53, 59 modulo 60. (End)

Examples

			7 is a term since 5^3 - 3^3 = 7*14.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index to sequences related to decomposition of primes in quadratic fields

Crossrefs

A038887, the sequence of primes that do not remain inert in the field Q(sqrt(15)), is essentially the same.

Cf. A038888 (rational primes that remain inert in the field Q(sqrt(15))).

Programs

Mathematica

Select[Prime[Range[150]],Divisible[5^((#-1)/2)-3^((#-1)/2),#]&] (* Harvey P. Dale, Apr 11 2018 *)

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, 5, 2, -1)

PARI

isA097956(p) == isprime(p) && kronecker(60, p) == 1 \\ Jianing Song, Oct 13 2022