Equation 677 Database

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Magma 70249bf6f30b…

magma 70249bf6f30b
Size
181
Isomorphism class hash
70249bf6f30b97f16867a295f6d738e462498dbbdac33235e7d483a37e89e6ad
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:26:47
Display reorder
0,1,105,141,38,164,123,72,10,93,51,25,34,17,87,148,110,9,61,40,45,104,54,5,97,140,173,23,91,20,107,81,160,163,158,154,7,122,133,102,31,85,55,30,2,63,111,89,98,92,161,62,69,57,99,16,180,75,144,37,88,42,116,137,143,70,156,82,19,52,44,66,53,147,178,167,24,109,113,118,115,71,152,3,136,6,128,95,142,22,43,149,32,60,41,77,155,103,68,76,47,8,29,138,78,13,168,119,58,96,150,18,26,139,120,36,28,172,80,171,59,73,175,84,146,90,64,170,177,79,131,4,166,106,124,86,74,46,48,174,108,159,134,49,112,162,100,145,117,157,27,179,114,153,129,35,33,15,67,169,151,121,21,176,11,132,125,83,135,101,65,130,14,39,126,12,127,50,56,165,94 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-181 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_181 (181 prime): x ◇ y = x + f(y − x) in F_181, where f(0) = 0, f(d) = 56·d when d is a quadratic residue mod 181, and f(d) = 122·d when d is a non-residue. So the multiplier on the difference y − x depends only on its QR/NQR class. The display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-181 magma automorphism τ (the hidden additive translation by 1 in F_181), making the magma fully translation-invariant in the rendered table: every row is a horizontal shift of row 0. [text written by Claude]

last edited by dwrensha at 2026-05-14 20:01:21 · history