Irreducible Polynomials Which Divide Trinomials Over GF(2). - The ...
Irreducible Polynomials Which Divide Trinomials Over GF(2). - The ...
Irreducible Polynomials Which Divide Trinomials Over GF(2). - The ...
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Table 3.4: Factors of Φ n (2) versus members of the multiplicative module M (2 ≤ n ≤ 61)n factorization of φ n (2) φ n (2) ∈ M? n factorization of φ n (2) φ n (2) ∈ M?2 3 Yes 32 65, 537 No3 7 Yes 33 599, 479 Yes4 5 No 34 43, 691 No5 31 Yes 35 71 · 122, 921 Yes6 3 Yes 36 37 · 109 No7 127 Yes 37 223 · 616, 318, 177 Yes8 17 No 38 174, 763 No9 73 Yes 39 79 · 121, 369 Yes10 11 No 40 61, 681 No11 23 · 89 Yes 41 164, 511, 353 · 13, 367 Yes12 13 No 42 5419 No13 8, 191 Yes 43 431 · 2, 099, 863 · 9, 719 Yes14 43 No 44 397 · 2, 113 No15 151 No 45 631 · 23, 311 Yes16 257 No 46 2, 796, 203 No17 131, 071 Yes 47 13, 264, 529 · 2, 351 · 4, 513 Yes18 3 · 19 Yes 48 97 · 673 No19 524, 287 Yes 49 4, 432, 676, 798, 593 Unknown20 5 · 41 No 50 251 · 4, 051 No21 7 · 337 Yes 51 103 · 11, 119 · 2, 143 Yes22 683 No 52 53 · 157 · 1, 613 No23 47 · 178, 481 Yes 53 69, 431 · 20, 394, 401 · 6, 361 Yes24 241 No 54 3 · 87, 211 Yes25 601 · 1, 801 No 55 881 · 3, 191 · 201, 961 Unknown26 2, 731 No 56 15, 790, 321 No27 262, 657 Yes 57 1, 212, 847 · 32, 377 Unknown28 29 · 113 No 58 59 · 3, 033, 169 Unknown29 233 · 1, 103 · 2, 089 Yes 59 3, 203, 431, 780, 337 · 179, 951 Yes30 331 No 60 61 · 1, 321 No31 2, 147, 483, 647 Yes 61 2, 305, 843, 009, 213, 693, 951 Yes38