A355962 Primes p such that (p+7)^(p-1) == 1 (mod p^2).

2, 3, 229, 701, 31446553, 1016476523, 8918351831

Offset: 1

Author

Felix Fröhlich, Jul 21 2022

Keywords

• nonn
• hard
• more

Comments

a(8) > 10^13 if it exists. - Jason Yuen, May 12 2024

Equivalently, primes p such that 7^p == p+7 (mod p^2), or Fermat quotient q_p(7) == 1/7 (mod p). - Max Alekseyev, Sep 16 2024

Crossrefs

(p+k)^(p-1) == 1 (mod p^2): A355959 (k=2), A355960 (k=5), A355961 (k=6), A355963 (k=8), A355964 (k=9), A355965 (k=10).

Programs

PARI

forprime(p=1, , if(Mod(p+7, p^2)^(p-1)==1, print1(p, ", ")))

Extensions

a(7) from Jason Yuen, May 12 2024