erdős #479
Is it true that, for all , there are infinitely many such that ?
Worked, still open.
number theory · open · formalized (Lean) · 0 attempts
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vela registry pull vfr_37aec80d874a0239vela reproduce examples/erdos-problemsevidence
unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
Not known in general — this is an open problem.
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗formal
AMS 11 · open (literature)
theorem erdos_479 : answer(sorry) ↔ ∀ᵉ (k > 1), { n | 2 ^ n ≡ k [MOD n]}.Infiniteformal-conjectures/479.lean ↗oeis
A006517 — Numbers k such that k divides 2^k + 2.1,2,6,66,946,8646,180246,199606,265826,383846,1234806,3757426,9880278,14304466,23612226,27052806,43091686,63265474,66154A006521 — Numbers n such that n divides 2^n + 1.1,3,9,27,81,171,243,513,729,1539,2187,3249,4617,6561,9747,13203,13851,19683,29241,39609,41553,59049,61731,87723,97641,11A015919 — Positive integers k such that 2^k == 2 (mod k).1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157A015921 — Positive integers n such that 2^n == 4 (mod n).1,2,4,6,10,12,14,22,26,30,34,38,46,58,62,74,82,86,94,106,118,122,132,134,142,146,158,166,170,178,182,194,202,206,214,218A015940 — Positive integers n such that 2^n == -3 (mod n).1,5,917,3223,62911,326329,395819,33504053,4446226763,17556128765,141613728437,5259417592253,113837290408523A036236 — Least inverse of A015910: smallest integer k > 0 such that 2^k mod k = n, or 0 if no such k exists.1,0,3,4700063497,6,19147,10669,25,9,2228071,18,262279,3763,95,1010,481,20,45,35,2873,2951,3175999,42,555,50,95921,27,174A050259 — Numbers k such that 2^k == 3 (mod k).1,4700063497,3468371109448915,8365386194032363,10991007971508067
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status
open