A327840 Numbers m that divide 4^m + 3.

1, 7, 16387, 4509253, 24265177, 42673920001, 103949349763, 12939780075073

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 27 2019

Keywords

• nonn
• more

Comments

Number of solutions < 10^9 to k^n == k-1 (mod n): 1 (if k = 1), 188 (if k = 2, see A006521), 5 (if k = 3, see A015973), 5 (if k = 4, see this sequence), 5 (if k = 5), 10 (if k = 6), 10 (if k = 7), 7 (if k = 8), 5 (if k = 9), 8 (if k = 10), 11 (if k = 11), 8 (if k = 12), 9 (if k = 13), 4 (if k = 14), 3 (if k = 15), 6 (if k = 16), 7 (if k = 17), 7 (if k = 18), ...

a(9) > 10^15. - Max Alekseyev, Nov 10 2022

Crossrefs

Solutions to k^n == 1-k (mod n): A006521 (k = 2), A015973 (k = 3), this sequence (k = 4), A123047 (k = 5), A327943 (k = 6).

Solutions to 4^n == k (mod n): A000079 (k = 0), A015950 (k = -1), A014945 (k = 1), A130421 (k = 2), this sequence (k = -3), A130422 (k = 3).

Cf. A015940, A253208.

Programs

Magma

[1] cat [n: n in [1..10^8] | Modexp(4,n,n) + 3 eq n];

Mathematica

Select[Range[10^7], IntegerQ[(PowerMod[4, #, # ]+3)/# ]&] (* Metin Sariyar, Sep 28 2019 *)

PARI

is(n)=Mod(4,n)^n==-3 \\ Charles R Greathouse IV, Sep 29 2019

Extensions

a(6)-a(7) from Giovanni Resta, Sep 29 2019

a(8) from Max Alekseyev, Nov 10 2022