A323705 Odd primes p such that ((p+1)/2)^(p-1) == 1 (mod p^2).

1897121, 52368101, 126233057

Offset: 1

Author

Felix Fröhlich, Jan 24 2019

Keywords

• nonn
• hard
• bref
• more

Comments

The corresponding sequence when (p+1) in the congruence is replaced with (p-1) seems to be A125854.

a(4) > 4262937421 if it exists.

Crossrefs

Cf. A125854, A259502.

Programs

Mathematica

Select[Prime[Range[718*10^4]],PowerMod[(#+1)/2,#-1,#^2]==1&] (* Harvey P. Dale, May 14 2021 *)

PARI

forprime(p=3, , my(x=(p+1)/2); if(Mod(x, p^2)^(p-1)==1, print1(p, ", ")))