Equation 677 Database

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Magma 039a065b060f…

magma 039a065b060f
Size
703
Isomorphism class hash
039a065b060f7ae3a1d0e93cc43fa41e49875237d0030dc8749ef6272c1c061e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 702) what is this?
Submitted by
dwrensha
Submitted at
2026-09-27 18:48:22
Display reorder
698,303,48,321,581,212,262,191,295,360,102,157,442,183,306,268,281,100,329,455,633,49,561,350,479,700,32,697,144,246,451,397,120,126,634,317,379,686,13,399,58,249,206,677,298,182,259,14,477,229,622,531,387,376,308,637,461,224,507,67,462,473,392,31,602,358,447,345,184,541,648,438,97,272,271,2,287,552,34,11,671,398,289,146,535,252,549,76,211,594,162,88,548,343,230,80,348,63,141,386,17,691,263,661,564,504,328,346,219,198,385,164,208,293,107,480,56,357,410,407,253,422,151,324,396,424,274,684,207,643,236,538,86,662,231,33,498,20,383,370,566,463,297,630,559,640,423,171,277,101,619,113,368,87,35,78,401,668,529,371,223,189,318,487,382,414,429,349,431,394,650,563,669,40,27,377,470,655,647,178,108,138,112,103,693,378,196,512,439,374,419,588,47,69,680,203,145,110,70,519,381,595,94,228,135,544,620,235,569,260,267,702,489,482,347,457,83,322,654,432,9,391,603,315,625,629,682,425,143,624,50,366,197,578,217,290,418,600,174,3,631,657,645,400,128,136,266,599,18,43,150,341,131,190,227,571,225,210,604,283,522,393,445,575,307,149,179,615,38,1,590,632,82,5,499,690,201,121,355,111,501,241,344,574,605,29,276,36,453,125,623,334,458,106,411,165,496,202,192,546,670,200,475,185,188,579,53,258,644,515,412,683,607,420,441,568,550,300,342,124,467,172,26,608,678,66,570,617,434,565,326,0,699,390,415,613,327,474,313,665,511,194,152,96,37,330,509,104,493,494,12,216,129,337,406,567,243,580,380,22,596,251,240,64,285,446,239,118,530,598,591,309,85,433,255,99,481,404,502,158,428,471,61,177,98,167,601,521,115,663,639,193,247,450,681,160,23,163,257,572,339,46,114,233,551,4,485,490,528,405,220,676,6,582,517,395,466,416,359,543,45,525,161,275,628,335,562,117,513,460,130,147,279,19,389,583,560,653,516,59,660,545,311,592,692,427,180,540,148,319,363,618,508,674,316,365,116,408,55,606,269,320,109,449,331,288,354,658,586,486,21,169,476,127,659,71,642,65,213,305,284,484,7,79,333,468,532,469,84,609,472,209,673,122,296,312,41,696,314,542,556,218,187,555,237,373,166,24,270,589,353,244,77,215,132,57,417,278,176,421,299,214,261,93,256,505,75,573,304,584,430,302,701,375,42,426,554,248,325,74,454,456,675,694,16,495,672,133,137,403,221,464,444,54,687,170,95,73,119,142,627,576,292,514,372,90,679,638,610,10,689,168,51,222,242,443,181,656,652,153,273,25,175,156,234,232,611,547,452,332,204,39,597,89,506,226,362,526,369,612,301,478,8,465,436,503,199,695,500,195,60,651,437,614,448,557,367,492,15,685,577,459,351,409,440,352,338,536,159,44,534,518,641,154,413,250,72,621,265,310,264,537,616,92,280,488,527,435,68,105,626,140,664,254,688,30,282,364,139,558,510,553,245,646,524,491,384,52,186,635,587,520,155,286,81,585,523,667,336,402,205,173,388,533,323,123,62,294,134,356,361,593,28,483,666,649,238,291,636,340,539,91,497 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Monogenic cyclic-affine Eq677 magma of order 703. On Z/703, in construction labels, x*y = 26x + 668y + 1 (mod 703). Element 0 generates the whole magma; there are 648 generators and 1 idempotent element(s). For any element r, the generated submagma has size 703/gcd(703, (26+668-1)r+1). Both coefficients are units modulo 703, so this is a quasigroup (left- and right-cancellative); its fiber matrix is all ones. The affine Eq677 conditions are ab(1+b^2)=1, a+a^2*b^2+b^3=0, and (b^2(a+1)+b+1)c=0 modulo n. These hold for the displayed parameters. Independently checked all 494209 Eq677 instances, all 703 Eq255 instances, and full set closure from generator 0 directly in the saved table. This is not a counterexample to Eq677 => Eq255. Found while enumerating monogenic cyclic-affine models of orders below 1000, working upward in order. These are standard affine constructions, added to fill gaps in the database. Construction labels may differ from the server canonical labels. Computed with OpenAI Codex working with dwrensha, 2026-09-27.

last edited by dwrensha at 2026-09-27 18:48:22 · history