cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A329222 Numbers m that divide 5^(m + 1) + 1.

Original entry on oeis.org

1, 2, 6, 13, 14, 174, 854, 2694, 78126, 103973, 106694, 121974, 420209, 487374, 1299374, 2174654, 3895094, 4151454, 5842214, 5951129, 6508334, 10637054, 20117894, 24482957, 31999694, 32282053, 32620202, 32872454, 34258454, 52657397, 56114618, 57679082, 65538437, 70782774, 71899526
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 08 2019

Keywords

Comments

Conjecture: For k > 1, k^(m + 1) == -1 (mod m) has an infinite number of positive solutions.

Crossrefs

Cf. A055685.
Solutions to k^(m + 1) == -1 (mod m): A296369 (k=2), A328230 (k=3), A329168 (k=4), this sequence (k=5), A329226 (k=6).

Programs

  • Magma
    [n + 1: n in [0..2000000] | Modexp(5, n + 2, n + 1) eq n];
  • Mathematica
    Select[Range[719*10^5],PowerMod[5,#+1,#]==#-1&] (* Harvey P. Dale, Jul 03 2020 *)
  • PARI
    isok(m) = Mod(5, m)^(m+1) == -1; \\ Jinyuan Wang, Nov 16 2019
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