A372771 Numbers m such that the congruence x^(m+1) == m (mod m+1) is solvable.

1, 2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 25, 26, 28, 30, 32, 33, 34, 36, 38, 40, 42, 44, 46, 48, 49, 50, 52, 54, 56, 57, 58, 60, 62, 64, 66, 68, 70, 72, 73, 74, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110

Offset

1,2

Comments

Includes all positive even numbers. - Robert Israel, Mar 14 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

9 is a term because x^(9+1) == 9 (mod 9+1) for x = 3 and x = 7, i.e., 3^10 = 59049 == 9 (mod 10) and 7^10 = 282475249 == 9 (mod 10).

Maple

select(m -> traperror(NumberTheory:-ModularRoot(m, m+1, m+1))::integer, [$1..200]); # Robert Israel, Mar 14 2025

Mathematica

Select[Range[1, 110], With[{m = #}, AnyTrue[Range[1, m + 1], PowerMod[#, m + 1, m + 1] == m &]] &] (* Robert P. P. McKone, May 14 2024 *)

Crossrefs

Cf. A014117, A330279, A371811.

Sequence in context: A296214 A325572 A337945 * A247423 A182339 A110262

Adjacent sequences: A372768 A372769 A372770 * A372772 A372773 A372774

Keyword

nonn,changed

Author

Juri-Stepan Gerasimov, May 12 2024

Extensions

Terms corrected by Robert P. P. McKone, May 14 2024

Status

approved