

A327840


Numbers m that divide 4^m + 3.


5




OFFSET

1,2


COMMENTS

Number of solutions < 10^9 to k^n == k1 (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


LINKS

Table of n, a(n) for n=1..8.


MATHEMATICA

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


PROG

(Magma) [1] cat [n: n in [1..10^8]  Modexp(4, n, n) + 3 eq n];
(PARI) is(n)=Mod(4, n)^n==3 \\ Charles R Greathouse IV, Sep 29 2019


CROSSREFS

Solutions to k^n == 1k (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.
Sequence in context: A280813 A203685 A134645 * A115997 A013786 A351326
Adjacent sequences: A327837 A327838 A327839 * A327841 A327842 A327843


KEYWORD

nonn,more


AUTHOR

JuriStepan Gerasimov, Sep 27 2019


EXTENSIONS

a(6)a(7) from Giovanni Resta, Sep 29 2019
a(8) from Max Alekseyev, Nov 10 2022


STATUS

approved



