Equation 677 Database

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Magma f14f808fdeba…

magma f14f808fdeba
Size
181
Isomorphism class hash
f14f808fdebadfb339ee419f3efd5fd9dc0bee42c6261f7a0c5328024e0a6c86
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:26:45
Display reorder
0,1,14,17,50,107,21,47,137,124,79,173,101,78,68,144,161,18,85,105,41,158,89,16,126,56,133,131,5,121,110,31,118,22,153,93,129,76,26,4,24,179,167,164,139,34,135,95,141,96,140,90,75,94,119,122,134,65,45,67,35,174,138,108,63,163,72,155,166,46,176,178,15,171,57,3,113,82,150,44,59,116,99,27,37,146,128,38,169,92,6,62,152,9,58,55,87,86,117,151,52,64,13,39,109,84,32,120,91,142,83,168,53,130,71,111,132,127,159,7,145,102,125,70,66,49,60,2,40,98,61,157,115,148,74,10,69,104,77,180,36,149,28,51,33,103,160,112,20,143,81,88,19,8,25,29,170,147,100,48,114,172,177,156,30,175,12,123,42,97,136,165,73,43,154,80,54,23,11,106,162 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) = 139·d when d is a quadratic residue mod 181, and f(d) = 46·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