A097957 Primes p such that p divides 5^((p-1)/2) + 4^((p-1)/2).

3, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 103, 107, 113, 127, 137, 157, 163, 167, 173, 193, 197, 223, 227, 233, 257, 263, 277, 283, 293, 307, 313, 317, 337, 347, 353, 367, 373, 383, 397, 433, 443, 457, 463, 467, 487, 503, 523, 547, 557, 563, 577, 587

Offset: 1

Author

Cino Hilliard, Sep 06 2004

Keywords

• nonn
• easy

Comments

Also odd primes congruent to {2, 3} mod 5, or primes with last digit 3 or 7. - Alexander Adamchuk, Nov 02 2006

5 is not a square mod p. - Michael Somos, Aug 15 2012

Examples

			5^3 + 4^3 = 7*27
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A003631 = Primes congruent to {2, 3} mod 5.

Programs

Mathematica

Select[Prime[Range[120]],Divisible[5^((#-1)/2)+4^((#-1)/2),#]&] (* Harvey P. Dale, Feb 25 2013 *)

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","))) }

PARI

{a(n) = local( cnt, m ); if( n<1, return( 0 )); while( cnt < n, if( isprime( m++) && kronecker( 20, m )== -1, cnt++ )); m} /* Michael Somos, Aug 15 2012 */

Formula

a(n) = A003631(n-1). - Alexander Adamchuk, Nov 02 2006

Extensions

Definition clarified by Harvey P. Dale, Feb 25 2013