-------------------------------------- 12 24 = X^8 - X^4 + X^0 1 * 2 * 2 = 1 * 1 * 5 -------------------------------------- 18 36 = X^12 - X^6 + X^0 1 * 2 * 3 = 1 * 1 * 10 2 * 2 * 3 = 1 * 2 * 8 1 * 3 * 4 = 1 * 2 * 7 2 * 2 * 4 = 1 * 3 * 6 2 * 3 * 3 = 1 * 4 * 5 -------------------------------------- 24 48 = X^16 - X^8 + X^0 2 * 2 * 4 = 1 * 2 * 13 2 * 3 * 4 = 1 * 3 * 11 2 * 3 * 5 = 1 * 4 * 9 2 * 4 * 4 = 2 * 2 * 10 3 * 3 * 4 = 1 * 6 * 7 1 * 4 * 6 = 1 * 3 * 9 -------------------------------------- 30 60 = X^16 + X^14 - X^10 - X^8 - X^6 + X^2 + X^0 1 * 2 * 4 = 1 * 1 * 21 2 * 3 * 3 = 1 * 2 * 19 1 * 4 * 5 = 1 * 2 * 17 2 * 3 * 5 = 1 * 3 * 16 1 * 3 * 7 = 1 * 2 * 16 2 * 4 * 5 = 1 * 4 * 14 3 * 4 * 4 = 1 * 5 * 13 2 * 2 * 8 = 1 * 3 * 14 2 * 3 * 7 = 2 * 2 * 14 2 * 4 * 6 = 1 * 5 * 12 3 * 3 * 6 = 1 * 6 * 11 3 * 4 * 5 = 1 * 8 * 9 3 * 4 * 5 = 2 * 3 * 13 1 * 4 * 8 = 1 * 3 * 13 2 * 3 * 8 = 1 * 5 * 11 2 * 4 * 7 = 1 * 7 * 9 2 * 5 * 6 = 2 * 3 * 12 3 * 5 * 5 = 2 * 4 * 11 1 * 5 * 8 = 1 * 4 * 11 1 * 6 * 7 = 2 * 2 * 12 2 * 3 * 9 = 1 * 7 * 8 3 * 4 * 7 = 2 * 5 * 9 3 * 5 * 6 = 2 * 6 * 8 4 * 5 * 5 = 3 * 4 * 9 2 * 5 * 8 = 3 * 3 * 9 3 * 3 * 9 = 2 * 5 * 8 -------------------------------------- 36 72 = X^24 - X^12 + X^0 2 * 4 * 6 = 1 * 4 * 19 2 * 4 * 6 = 2 * 2 * 20 2 * 5 * 6 = 1 * 5 * 17 2 * 5 * 7 = 1 * 6 * 15 3 * 4 * 7 = 1 * 8 * 13 3 * 5 * 6 = 1 * 10 * 11 4 * 4 * 6 = 2 * 4 * 16 3 * 6 * 6 = 3 * 3 * 15 2 * 6 * 8 = 2 * 4 * 14 4 * 4 * 8 = 2 * 6 * 12 4 * 6 * 6 = 2 * 8 * 10 1 * 6 * 10 = 1 * 5 * 13 -------------------------------------- 42 84 = X^24 + X^22 - X^18 - X^16 + X^12 - X^8 - X^6 + X^2 + X^0 1 * 3 * 9 = 1 * 2 * 26 1 * 6 * 7 = 1 * 3 * 24 2 * 5 * 7 = 1 * 5 * 22 3 * 4 * 7 = 2 * 3 * 23 2 * 6 * 7 = 1 * 6 * 20 3 * 4 * 8 = 1 * 7 * 19 2 * 6 * 8 = 1 * 7 * 18 3 * 5 * 8 = 1 * 10 * 15 3 * 6 * 7 = 1 * 12 * 13 4 * 5 * 7 = 2 * 5 * 19 2 * 7 * 8 = 1 * 9 * 15 4 * 6 * 7 = 3 * 4 * 18 3 * 6 * 9 = 2 * 6 * 16 3 * 7 * 8 = 3 * 4 * 17 4 * 5 * 9 = 2 * 7 * 15 5 * 6 * 7 = 2 * 10 * 12 2 * 7 * 10 = 2 * 5 * 16 3 * 7 * 9 = 2 * 8 * 13 4 * 5 * 10 = 3 * 5 * 15 1 * 7 * 12 = 1 * 6 * 15 1 * 9 * 10 = 2 * 3 * 17 4 * 6 * 10 = 3 * 7 * 12 4 * 7 * 9 = 3 * 8 * 11 1 * 7 * 13 = 2 * 3 * 16 2 * 3 * 16 = 1 * 7 * 13 -------------------------------------- 48 96 = X^32 - X^16 + X^0 2 * 6 * 8 = 1 * 6 * 25 2 * 6 * 8 = 2 * 3 * 27 4 * 4 * 8 = 2 * 4 * 26 2 * 7 * 8 = 1 * 7 * 23 2 * 7 * 9 = 1 * 8 * 21 3 * 6 * 9 = 1 * 12 * 17 3 * 7 * 8 = 1 * 14 * 15 4 * 6 * 8 = 2 * 6 * 22 5 * 6 * 8 = 3 * 5 * 21 4 * 6 * 10 = 2 * 8 * 18 4 * 8 * 8 = 4 * 4 * 20 6 * 6 * 8 = 2 * 12 * 14 3 * 8 * 10 = 3 * 5 * 19 2 * 8 * 12 = 2 * 6 * 18 2 * 9 * 11 = 3 * 4 * 19 5 * 6 * 11 = 3 * 8 * 15 5 * 8 * 9 = 3 * 10 * 13 1 * 8 * 14 = 1 * 7 * 17 -------------------------------------- 54 108 = X^36 - X^18 + X^0 1 * 8 * 9 = 1 * 4 * 31 2 * 7 * 9 = 1 * 7 * 28 3 * 6 * 9 = 3 * 3 * 30 4 * 5 * 9 = 2 * 5 * 29 2 * 8 * 9 = 1 * 8 * 26 2 * 8 * 10 = 1 * 9 * 24 3 * 7 * 10 = 1 * 14 * 19 3 * 8 * 9 = 1 * 16 * 17 4 * 7 * 9 = 2 * 7 * 25 6 * 6 * 9 = 3 * 6 * 24 4 * 7 * 11 = 2 * 9 * 21 5 * 6 * 11 = 2 * 10 * 20 5 * 8 * 9 = 4 * 5 * 23 6 * 7 * 9 = 2 * 14 * 16 4 * 9 * 10 = 4 * 5 * 22 3 * 9 * 12 = 3 * 6 * 21 6 * 6 * 12 = 3 * 9 * 18 6 * 9 * 9 = 3 * 12 * 15 2 * 9 * 14 = 2 * 7 * 20 1 * 9 * 16 = 1 * 8 * 19 1 * 12 * 13 = 2 * 4 * 22 5 * 8 * 13 = 4 * 9 * 15 5 * 9 * 12 = 4 * 10 * 14 -------------------------------------- 60 120 = X^32 + X^28 - X^20 - X^16 - X^12 + X^4 + X^0 2 * 4 * 8 = 2 * 2 * 42 4 * 6 * 6 = 2 * 4 * 38 4 * 6 * 8 = 1 * 10 * 31 4 * 6 * 8 = 2 * 5 * 35 5 * 6 * 8 = 1 * 13 * 27 2 * 8 * 10 = 1 * 8 * 31 2 * 8 * 10 = 2 * 4 * 34 4 * 6 * 10 = 2 * 6 * 32 4 * 6 * 10 = 3 * 4 * 33 4 * 7 * 9 = 1 * 14 * 25 5 * 6 * 9 = 1 * 16 * 23 5 * 7 * 8 = 1 * 18 * 21 2 * 9 * 10 = 1 * 9 * 29 3 * 8 * 10 = 1 * 13 * 25 2 * 4 * 16 = 1 * 6 * 31 2 * 4 * 16 = 2 * 3 * 33 2 * 6 * 14 = 2 * 4 * 32 2 * 9 * 11 = 1 * 10 * 27 3 * 8 * 11 = 1 * 16 * 21 3 * 9 * 10 = 1 * 18 * 19 4 * 8 * 10 = 2 * 8 * 28 6 * 8 * 8 = 2 * 10 * 26 4 * 6 * 13 = 3 * 5 * 29 6 * 7 * 10 = 3 * 7 * 27 2 * 5 * 17 = 1 * 8 * 27 3 * 4 * 17 = 1 * 10 * 25 3 * 5 * 16 = 1 * 13 * 22 4 * 4 * 16 = 2 * 6 * 28 4 * 6 * 14 = 4 * 4 * 28 4 * 8 * 12 = 2 * 10 * 24 6 * 6 * 12 = 2 * 12 * 22 6 * 8 * 10 = 2 * 16 * 18 6 * 8 * 10 = 4 * 6 * 26 3 * 5 * 17 = 1 * 16 * 18 4 * 5 * 16 = 3 * 5 * 27 5 * 10 * 10 = 5 * 5 * 25 2 * 8 * 16 = 2 * 6 * 26 4 * 6 * 16 = 2 * 10 * 22 4 * 8 * 14 = 2 * 14 * 18 4 * 9 * 13 = 3 * 8 * 23 4 * 10 * 12 = 4 * 6 * 24 6 * 7 * 13 = 3 * 10 * 21 6 * 10 * 10 = 4 * 8 * 22 7 * 9 * 10 = 3 * 14 * 17 3 * 6 * 18 = 3 * 5 * 25 3 * 10 * 14 = 3 * 7 * 23 2 * 7 * 19 = 3 * 4 * 25 2 * 10 * 16 = 2 * 8 * 22 2 * 12 * 14 = 4 * 4 * 24 4 * 5 * 19 = 3 * 6 * 23 4 * 6 * 18 = 2 * 14 * 16 4 * 11 * 13 = 5 * 6 * 21 5 * 7 * 16 = 3 * 11 * 18 6 * 8 * 14 = 4 * 10 * 18 6 * 9 * 13 = 5 * 8 * 19 6 * 10 * 12 = 4 * 12 * 16 8 * 9 * 11 = 5 * 10 * 17 8 * 10 * 10 = 6 * 8 * 18 1 * 10 * 18 = 1 * 9 * 21 4 * 10 * 16 = 6 * 6 * 18 6 * 6 * 18 = 4 * 10 * 16 -------------------------------------- -------------------------------------- 66 132 = X^40 + X^38 - X^34 - X^32 + X^28 + X^26 - X^22 - X^20 - X^18 + X^14 + X^12 - X^8 - X^6 + X^2 + X^0 1 * 10 * 11 = 1 * 5 * 38 2 * 9 * 11 = 1 * 9 * 34 3 * 8 * 11 = 3 * 4 * 37 4 * 7 * 11 = 2 * 7 * 35 5 * 6 * 11 = 3 * 5 * 36 2 * 10 * 11 = 1 * 10 * 32 2 * 10 * 12 = 1 * 11 * 30 3 * 9 * 12 = 1 * 18 * 23 3 * 10 * 11 = 1 * 20 * 21 4 * 9 * 11 = 2 * 9 * 31 6 * 8 * 11 = 3 * 8 * 30 4 * 9 * 13 = 2 * 11 * 27 6 * 7 * 13 = 2 * 14 * 24 6 * 9 * 11 = 2 * 18 * 20 7 * 8 * 11 = 4 * 7 * 29 6 * 10 * 11 = 5 * 6 * 28 5 * 9 * 14 = 3 * 10 * 25 5 * 11 * 12 = 5 * 6 * 27 6 * 8 * 14 = 3 * 11 * 24 8 * 9 * 11 = 3 * 16 * 19 4 * 11 * 14 = 4 * 7 * 26 3 * 11 * 16 = 3 * 8 * 25 3 * 12 * 15 = 4 * 6 * 26 7 * 8 * 15 = 4 * 11 * 21 7 * 11 * 12 = 4 * 14 * 18 2 * 11 * 18 = 2 * 9 * 24 1 * 11 * 20 = 1 * 10 * 23 1 * 15 * 16 = 2 * 5 * 27 6 * 10 * 16 = 5 * 11 * 18 6 * 11 * 15 = 5 * 12 * 17 -------------------------------------- 72 144 = X^48 - X^24 + X^0 2 * 10 * 12 = 1 * 10 * 37 2 * 10 * 12 = 2 * 5 * 41 4 * 8 * 12 = 2 * 8 * 38 4 * 8 * 12 = 4 * 4 * 40 6 * 6 * 12 = 3 * 6 * 39 2 * 11 * 12 = 1 * 11 * 35 2 * 11 * 13 = 1 * 12 * 33 3 * 10 * 13 = 1 * 20 * 25 3 * 11 * 12 = 1 * 22 * 23 4 * 10 * 12 = 2 * 10 * 34 6 * 9 * 12 = 3 * 9 * 33 4 * 10 * 14 = 2 * 12 * 30 6 * 8 * 14 = 2 * 16 * 26 6 * 10 * 12 = 2 * 20 * 22 8 * 8 * 12 = 4 * 8 * 32 7 * 10 * 12 = 5 * 7 * 31 6 * 9 * 15 = 3 * 12 * 27 6 * 12 * 12 = 6 * 6 * 30 9 * 9 * 12 = 3 * 18 * 21 5 * 12 * 14 = 5 * 7 * 29 4 * 12 * 16 = 4 * 8 * 28 8 * 8 * 16 = 4 * 12 * 24 8 * 12 * 12 = 4 * 16 * 20 3 * 12 * 18 = 3 * 9 * 27 2 * 12 * 20 = 2 * 10 * 26 2 * 15 * 17 = 4 * 5 * 29 7 * 10 * 17 = 5 * 12 * 21 7 * 12 * 15 = 5 * 14 * 19 1 * 12 * 22 = 1 * 11 * 25 -------------------------------------- 78 156 = X^48 + X^46 - X^42 - X^40 + X^36 + X^34 - X^30 - X^28 + X^24 - X^20 - X^18 + X^14 + X^12 - X^8 - X^6 + X^2 + X^0 1 * 12 * 13 = 1 * 6 * 45 2 * 11 * 13 = 1 * 11 * 40 3 * 10 * 13 = 3 * 5 * 44 4 * 9 * 13 = 2 * 9 * 41 5 * 8 * 13 = 4 * 5 * 43 6 * 7 * 13 = 3 * 7 * 42 2 * 12 * 13 = 1 * 12 * 38 2 * 12 * 14 = 1 * 13 * 36 3 * 11 * 14 = 1 * 22 * 27 3 * 12 * 13 = 1 * 24 * 25 4 * 11 * 13 = 2 * 11 * 37 6 * 10 * 13 = 3 * 10 * 36 4 * 11 * 15 = 2 * 13 * 33 6 * 9 * 15 = 2 * 18 * 28 6 * 11 * 13 = 2 * 22 * 24 8 * 9 * 13 = 4 * 9 * 35 8 * 10 * 13 = 5 * 8 * 34 6 * 10 * 16 = 3 * 13 * 30 7 * 9 * 16 = 3 * 14 * 29 7 * 12 * 13 = 6 * 7 * 33 9 * 10 * 13 = 3 * 20 * 23 6 * 13 * 14 = 6 * 7 * 32 5 * 12 * 17 = 4 * 10 * 30 5 * 13 * 16 = 5 * 8 * 31 8 * 9 * 17 = 4 * 13 * 27 9 * 12 * 13 = 4 * 18 * 22 4 * 13 * 18 = 4 * 9 * 30 3 * 13 * 20 = 3 * 10 * 29 3 * 15 * 18 = 5 * 6 * 31 8 * 10 * 18 = 5 * 13 * 24 8 * 13 * 15 = 5 * 16 * 21 2 * 13 * 22 = 2 * 11 * 28 1 * 13 * 24 = 1 * 12 * 27 1 * 18 * 19 = 2 * 6 * 32 7 * 12 * 19 = 6 * 13 * 21 7 * 13 * 18 = 6 * 14 * 20 -------------------------------------- 84 168 = X^48 + X^44 - X^36 - X^32 + X^24 - X^16 - X^12 + X^4 + X^0 2 * 6 * 18 = 2 * 4 * 52 4 * 6 * 16 = 1 * 14 * 43 4 * 6 * 16 = 2 * 7 * 49 2 * 12 * 14 = 1 * 12 * 43 2 * 12 * 14 = 2 * 6 * 48 4 * 7 * 17 = 1 * 18 * 37 4 * 10 * 14 = 2 * 10 * 44 4 * 10 * 14 = 4 * 5 * 47 5 * 6 * 17 = 1 * 20 * 35 5 * 7 * 16 = 1 * 25 * 30 6 * 8 * 14 = 3 * 8 * 45 6 * 8 * 14 = 4 * 6 * 46 2 * 13 * 14 = 1 * 13 * 41 2 * 13 * 15 = 1 * 14 * 39 3 * 12 * 15 = 1 * 24 * 29 3 * 13 * 14 = 1 * 26 * 27 4 * 12 * 14 = 2 * 12 * 40 6 * 8 * 16 = 2 * 14 * 38 6 * 11 * 14 = 3 * 11 * 39 4 * 12 * 16 = 2 * 14 * 36 6 * 10 * 16 = 2 * 20 * 30 6 * 12 * 14 = 2 * 24 * 26 8 * 10 * 14 = 4 * 10 * 38 9 * 10 * 14 = 5 * 9 * 37 4 * 14 * 16 = 2 * 18 * 30 6 * 11 * 17 = 3 * 14 * 33 8 * 9 * 17 = 3 * 16 * 31 8 * 12 * 14 = 6 * 8 * 36 9 * 11 * 14 = 3 * 22 * 25 7 * 14 * 14 = 7 * 7 * 35 6 * 12 * 18 = 4 * 12 * 32 6 * 14 * 16 = 6 * 8 * 34 8 * 10 * 18 = 4 * 14 * 30 10 * 12 * 14 = 4 * 20 * 24 5 * 14 * 18 = 5 * 9 * 33 4 * 14 * 20 = 4 * 10 * 32 4 * 15 * 19 = 5 * 8 * 33 6 * 14 * 18 = 4 * 16 * 26 8 * 10 * 20 = 6 * 10 * 30 9 * 10 * 19 = 5 * 14 * 27 9 * 14 * 15 = 5 * 18 * 23 3 * 14 * 22 = 3 * 11 * 31 2 * 14 * 24 = 2 * 12 * 30 2 * 18 * 20 = 4 * 6 * 34 4 * 13 * 23 = 6 * 7 * 31 6 * 11 * 23 = 7 * 8 * 29 8 * 12 * 20 = 6 * 14 * 24 8 * 14 * 18 = 6 * 16 * 22 11 * 13 * 16 = 7 * 18 * 19 1 * 14 * 26 = 1 * 13 * 29 2 * 14 * 26 = 4 * 6 * 32 4 * 6 * 32 = 2 * 14 * 26 -------------------------------------- 90 180 = X^48 + X^42 - X^30 - X^24 - X^18 + X^6 + X^0 3 * 6 * 12 = 3 * 3 * 63 6 * 9 * 9 = 3 * 6 * 57 5 * 8 * 12 = 1 * 17 * 47 1 * 14 * 15 = 1 * 7 * 52 2 * 13 * 15 = 1 * 13 * 46 3 * 12 * 15 = 3 * 6 * 51 4 * 11 * 15 = 2 * 11 * 47 5 * 10 * 15 = 5 * 5 * 50 6 * 9 * 15 = 3 * 9 * 48 7 * 8 * 15 = 4 * 7 * 49 2 * 14 * 15 = 1 * 14 * 44 2 * 14 * 16 = 1 * 15 * 42 3 * 13 * 16 = 1 * 26 * 31 3 * 14 * 15 = 1 * 28 * 29 4 * 13 * 15 = 2 * 13 * 43 3 * 9 * 21 = 3 * 6 * 48 6 * 12 * 15 = 3 * 12 * 42 9 * 12 * 12 = 3 * 15 * 39 4 * 13 * 17 = 2 * 15 * 39 6 * 11 * 17 = 2 * 22 * 32 6 * 13 * 15 = 2 * 26 * 28 8 * 11 * 15 = 4 * 11 * 41 4 * 6 * 25 = 1 * 23 * 31 10 * 10 * 15 = 5 * 10 * 40 6 * 6 * 24 = 3 * 9 * 42 6 * 9 * 21 = 6 * 6 * 42 6 * 12 * 18 = 3 * 15 * 36 9 * 9 * 18 = 3 * 18 * 33 9 * 12 * 15 = 3 * 24 * 27 9 * 12 * 15 = 6 * 9 * 39 5 * 9 * 23 = 2 * 19 * 32 8 * 14 * 15 = 7 * 8 * 38 11 * 12 * 14 = 5 * 13 * 35 7 * 12 * 19 = 4 * 14 * 34 7 * 15 * 16 = 7 * 8 * 37 8 * 11 * 19 = 4 * 15 * 33 11 * 12 * 15 = 4 * 22 * 26 3 * 12 * 24 = 3 * 9 * 39 6 * 9 * 24 = 3 * 15 * 33 6 * 12 * 21 = 3 * 21 * 27 6 * 15 * 18 = 6 * 9 * 36 9 * 15 * 15 = 6 * 12 * 33 5 * 15 * 20 = 5 * 10 * 35 10 * 10 * 20 = 5 * 15 * 30 10 * 15 * 15 = 5 * 20 * 25 4 * 15 * 22 = 4 * 11 * 34 3 * 15 * 24 = 3 * 12 * 33 3 * 18 * 21 = 6 * 6 * 36 6 * 9 * 27 = 3 * 21 * 24 9 * 12 * 21 = 6 * 15 * 27 9 * 15 * 18 = 6 * 18 * 24 12 * 15 * 15 = 9 * 12 * 27 2 * 15 * 26 = 2 * 13 * 32 1 * 15 * 28 = 1 * 14 * 31 1 * 21 * 22 = 2 * 7 * 37 8 * 14 * 22 = 7 * 15 * 24 8 * 15 * 21 = 7 * 16 * 23 6 * 15 * 24 = 9 * 9 * 27 9 * 9 * 27 = 6 * 15 * 24 -------------------------------------- -------------------------------------- 96 192 = X^64 - X^32 + X^0 2 * 14 * 16 = 1 * 14 * 49 2 * 14 * 16 = 2 * 7 * 55 4 * 12 * 16 = 2 * 12 * 50 4 * 12 * 16 = 4 * 6 * 54 6 * 10 * 16 = 3 * 10 * 51 6 * 10 * 16 = 5 * 6 * 53 8 * 8 * 16 = 4 * 8 * 52 2 * 15 * 16 = 1 * 15 * 47 2 * 15 * 17 = 1 * 16 * 45 3 * 14 * 17 = 1 * 28 * 33 3 * 15 * 16 = 1 * 30 * 31 4 * 14 * 16 = 2 * 14 * 46 6 * 13 * 16 = 3 * 13 * 45 4 * 14 * 18 = 2 * 16 * 42 6 * 12 * 18 = 2 * 24 * 34 6 * 14 * 16 = 2 * 28 * 30 8 * 12 * 16 = 4 * 12 * 44 10 * 11 * 16 = 5 * 11 * 43 6 * 13 * 19 = 3 * 16 * 39 9 * 10 * 19 = 3 * 20 * 35 9 * 13 * 16 = 3 * 26 * 29 10 * 12 * 16 = 6 * 10 * 42 9 * 14 * 16 = 7 * 9 * 41 8 * 12 * 20 = 4 * 16 * 36 8 * 16 * 16 = 8 * 8 * 40 12 * 12 * 16 = 4 * 24 * 28 7 * 16 * 18 = 7 * 9 * 39 6 * 15 * 21 = 5 * 12 * 37 6 * 16 * 20 = 6 * 10 * 38 10 * 11 * 21 = 5 * 16 * 33 11 * 15 * 16 = 5 * 22 * 27 5 * 16 * 22 = 5 * 11 * 37 4 * 16 * 24 = 4 * 12 * 36 4 * 18 * 22 = 6 * 8 * 38 10 * 12 * 22 = 6 * 16 * 30 10 * 16 * 18 = 6 * 20 * 26 3 * 16 * 26 = 3 * 13 * 35 2 * 16 * 28 = 2 * 14 * 34 2 * 21 * 23 = 4 * 7 * 39 9 * 14 * 23 = 7 * 16 * 27 9 * 16 * 21 = 7 * 18 * 25 1 * 16 * 30 = 1 * 15 * 33 -------------------------------------- 102 204 = X^64 + X^62 - X^58 - X^56 + X^52 + X^50 - X^46 - X^44 + X^40 + X^38 - X^34 - X^32 - X^30 + X^26 + X^24 - X^20 - X^18 + X^14 + X^12 - X^8 - X^6 + X^2 + X^0 1 * 16 * 17 = 1 * 8 * 59 2 * 15 * 17 = 1 * 15 * 52 3 * 14 * 17 = 3 * 7 * 58 4 * 13 * 17 = 2 * 13 * 53 5 * 12 * 17 = 5 * 6 * 57 6 * 11 * 17 = 3 * 11 * 54 7 * 10 * 17 = 5 * 7 * 56 8 * 9 * 17 = 4 * 9 * 55 2 * 16 * 17 = 1 * 16 * 50 2 * 16 * 18 = 1 * 17 * 48 3 * 15 * 18 = 1 * 30 * 35 3 * 16 * 17 = 1 * 32 * 33 4 * 15 * 17 = 2 * 15 * 49 6 * 14 * 17 = 3 * 14 * 48 4 * 15 * 19 = 2 * 17 * 45 6 * 13 * 19 = 2 * 26 * 36 6 * 15 * 17 = 2 * 30 * 32 8 * 13 * 17 = 4 * 13 * 47 10 * 12 * 17 = 5 * 12 * 46 6 * 14 * 20 = 3 * 17 * 42 9 * 11 * 20 = 3 * 22 * 37 9 * 14 * 17 = 3 * 28 * 31 11 * 12 * 17 = 6 * 11 * 45 10 * 14 * 17 = 7 * 10 * 44 8 * 13 * 21 = 4 * 17 * 39 9 * 12 * 21 = 4 * 18 * 38 9 * 16 * 17 = 8 * 9 * 43 12 * 13 * 17 = 4 * 26 * 30 8 * 17 * 18 = 8 * 9 * 42 7 * 15 * 22 = 5 * 14 * 39 7 * 17 * 20 = 7 * 10 * 41 10 * 12 * 22 = 5 * 17 * 36 12 * 15 * 17 = 5 * 24 * 29 6 * 17 * 22 = 6 * 11 * 40 5 * 17 * 24 = 5 * 12 * 39 5 * 18 * 23 = 6 * 10 * 40 11 * 12 * 23 = 6 * 17 * 33 11 * 17 * 18 = 6 * 22 * 28 4 * 17 * 26 = 4 * 13 * 38 3 * 17 * 28 = 3 * 14 * 37 3 * 21 * 24 = 6 * 7 * 41 10 * 14 * 24 = 7 * 17 * 30 10 * 17 * 21 = 7 * 20 * 27 2 * 17 * 30 = 2 * 15 * 36 1 * 17 * 32 = 1 * 16 * 35 1 * 24 * 25 = 2 * 8 * 42 9 * 16 * 25 = 8 * 17 * 27 9 * 17 * 24 = 8 * 18 * 26 -------------------------------------- 108 216 = X^72 - X^36 + X^0 2 * 16 * 18 = 1 * 16 * 55 2 * 16 * 18 = 2 * 8 * 62 4 * 14 * 18 = 2 * 14 * 56 4 * 14 * 18 = 4 * 7 * 61 6 * 12 * 18 = 3 * 12 * 57 6 * 12 * 18 = 6 * 6 * 60 8 * 10 * 18 = 4 * 10 * 58 8 * 10 * 18 = 5 * 8 * 59 2 * 17 * 18 = 1 * 17 * 53 2 * 17 * 19 = 1 * 18 * 51 3 * 16 * 19 = 1 * 32 * 37 3 * 17 * 18 = 1 * 34 * 35 4 * 16 * 18 = 2 * 16 * 52 6 * 15 * 18 = 3 * 15 * 51 4 * 16 * 20 = 2 * 18 * 48 6 * 14 * 20 = 2 * 28 * 38 6 * 16 * 18 = 2 * 32 * 34 8 * 14 * 18 = 4 * 14 * 50 10 * 13 * 18 = 5 * 13 * 49 6 * 15 * 21 = 3 * 18 * 45 9 * 12 * 21 = 3 * 24 * 39 9 * 15 * 18 = 3 * 30 * 33 12 * 12 * 18 = 6 * 12 * 48 11 * 14 * 18 = 7 * 11 * 47 8 * 14 * 22 = 4 * 18 * 42 10 * 12 * 22 = 4 * 20 * 40 10 * 16 * 18 = 8 * 10 * 46 12 * 14 * 18 = 4 * 28 * 32 9 * 18 * 18 = 9 * 9 * 45 8 * 15 * 23 = 5 * 16 * 41 8 * 18 * 20 = 8 * 10 * 44 10 * 13 * 23 = 5 * 18 * 39 13 * 15 * 18 = 5 * 26 * 31 7 * 18 * 22 = 7 * 11 * 43 6 * 18 * 24 = 6 * 12 * 42 12 * 12 * 24 = 6 * 18 * 36 12 * 18 * 18 = 6 * 24 * 30 5 * 18 * 26 = 5 * 13 * 41 4 * 18 * 28 = 4 * 14 * 40 4 * 21 * 25 = 7 * 8 * 43 11 * 14 * 25 = 7 * 18 * 33 11 * 18 * 21 = 7 * 22 * 29 3 * 18 * 30 = 3 * 15 * 39 2 * 18 * 32 = 2 * 16 * 38 2 * 24 * 26 = 4 * 8 * 44 10 * 16 * 26 = 8 * 18 * 30 10 * 18 * 24 = 8 * 20 * 28 1 * 18 * 34 = 1 * 17 * 37 -------------------------------------- 114 228 = X^72 + X^70 - X^66 - X^64 + X^60 + X^58 - X^54 - X^52 + X^48 + X^46 - X^42 - X^40 + X^36 - X^32 - X^30 + X^26 + X^24 - X^20 - X^18 + X^14 + X^ 12 - X^8 - X^6 + X^2 + X^0 1 * 18 * 19 = 1 * 9 * 66 2 * 17 * 19 = 1 * 17 * 58 3 * 16 * 19 = 3 * 8 * 65 4 * 15 * 19 = 2 * 15 * 59 5 * 14 * 19 = 5 * 7 * 64 6 * 13 * 19 = 3 * 13 * 60 7 * 12 * 19 = 6 * 7 * 63 8 * 11 * 19 = 4 * 11 * 61 9 * 10 * 19 = 5 * 9 * 62 2 * 18 * 19 = 1 * 18 * 56 2 * 18 * 20 = 1 * 19 * 54 3 * 17 * 20 = 1 * 34 * 39 3 * 18 * 19 = 1 * 36 * 37 4 * 17 * 19 = 2 * 17 * 55 6 * 16 * 19 = 3 * 16 * 54 4 * 17 * 21 = 2 * 19 * 51 6 * 15 * 21 = 2 * 30 * 40 6 * 17 * 19 = 2 * 34 * 36 8 * 15 * 19 = 4 * 15 * 53 10 * 14 * 19 = 5 * 14 * 52 6 * 16 * 22 = 3 * 19 * 48 9 * 13 * 22 = 3 * 26 * 41 9 * 16 * 19 = 3 * 32 * 35 12 * 13 * 19 = 6 * 13 * 51 12 * 14 * 19 = 7 * 12 * 50 8 * 15 * 23 = 4 * 19 * 45 11 * 12 * 23 = 4 * 22 * 42 11 * 16 * 19 = 8 * 11 * 49 12 * 15 * 19 = 4 * 30 * 34 10 * 18 * 19 = 9 * 10 * 48 9 * 15 * 24 = 5 * 18 * 43 9 * 19 * 20 = 9 * 10 * 47 10 * 14 * 24 = 5 * 19 * 42 14 * 15 * 19 = 5 * 28 * 33 8 * 19 * 22 = 8 * 11 * 46 7 * 18 * 25 = 6 * 14 * 44 7 * 19 * 24 = 7 * 12 * 45 12 * 13 * 25 = 6 * 19 * 39 13 * 18 * 19 = 6 * 26 * 32 6 * 19 * 26 = 6 * 13 * 44 5 * 19 * 28 = 5 * 14 * 43 5 * 21 * 26 = 7 * 10 * 45 12 * 14 * 26 = 7 * 19 * 36 12 * 19 * 21 = 7 * 24 * 31 4 * 19 * 30 = 4 * 15 * 42 3 * 19 * 32 = 3 * 16 * 41 3 * 24 * 27 = 6 * 8 * 46 11 * 16 * 27 = 8 * 19 * 33 11 * 19 * 24 = 8 * 22 * 30 2 * 19 * 34 = 2 * 17 * 40 1 * 19 * 36 = 1 * 18 * 39 1 * 27 * 28 = 2 * 9 * 47 10 * 18 * 28 = 9 * 19 * 30 10 * 19 * 27 = 9 * 20 * 29 -------------------------------------- 120 240 = X^64 + X^56 - X^40 - X^32 - X^24 + X^8 + X^0 4 * 8 * 16 = 4 * 4 * 84 6 * 10 * 16 = 1 * 26 * 61 6 * 10 * 16 = 2 * 13 * 73 8 * 12 * 12 = 4 * 8 * 76 6 * 11 * 17 = 1 * 32 * 53 7 * 10 * 17 = 1 * 36 * 49 7 * 11 * 16 = 1 * 42 * 43 8 * 12 * 16 = 2 * 20 * 62 8 * 12 * 16 = 4 * 10 * 70 10 * 12 * 16 = 2 * 26 * 54 2 * 18 * 20 = 1 * 18 * 61 2 * 18 * 20 = 2 * 9 * 69 4 * 16 * 20 = 2 * 16 * 62 4 * 16 * 20 = 4 * 8 * 68 6 * 14 * 20 = 3 * 14 * 63 6 * 14 * 20 = 6 * 7 * 67 8 * 12 * 20 = 4 * 12 * 64 8 * 12 * 20 = 6 * 8 * 66 8 * 14 * 18 = 2 * 28 * 50 10 * 10 * 20 = 5 * 10 * 65 10 * 12 * 18 = 2 * 32 * 46 10 * 14 * 16 = 2 * 36 * 42 2 * 19 * 20 = 1 * 19 * 59 2 * 19 * 21 = 1 * 20 * 57 3 * 18 * 21 = 1 * 36 * 41 3 * 19 * 20 = 1 * 38 * 39 4 * 18 * 20 = 2 * 18 * 58 6 * 16 * 20 = 2 * 26 * 50 6 * 17 * 20 = 3 * 17 * 57 4 * 8 * 32 = 2 * 12 * 62 4 * 8 * 32 = 4 * 6 * 66 4 * 12 * 28 = 4 * 8 * 64 4 * 18 * 22 = 2 * 20 * 54 6 * 16 * 22 = 2 * 32 * 42 6 * 18 * 20 = 2 * 36 * 38 8 * 16 * 20 = 4 * 16 * 56 12 * 16 * 16 = 4 * 20 * 52 10 * 15 * 20 = 5 * 15 * 55 6 * 17 * 23 = 3 * 20 * 51 8 * 12 * 26 = 6 * 10 * 58 9 * 14 * 23 = 3 * 28 * 43 9 * 17 * 20 = 3 * 34 * 37 12 * 14 * 20 = 6 * 14 * 54 13 * 14 * 20 = 7 * 13 * 53 4 * 10 * 34 = 2 * 16 * 54 6 * 8 * 34 = 2 * 20 * 50 6 * 10 * 32 = 2 * 26 * 44 8 * 8 * 32 = 4 * 12 * 56 8 * 12 * 28 = 8 * 8 * 56 8 * 16 * 24 = 4 * 20 * 48 12 * 12 * 24 = 4 * 24 * 44 12 * 16 * 20 = 4 * 32 * 36 12 * 16 * 20 = 8 * 12 * 52 11 * 18 * 20 = 9 * 11 * 51 6 * 10 * 34 = 2 * 32 * 36 8 * 10 * 32 = 6 * 10 * 54 10 * 15 * 25 = 5 * 20 * 45 10 * 20 * 20 = 10 * 10 * 50 15 * 15 * 20 = 5 * 30 * 35 9 * 20 * 22 = 9 * 11 * 49 4 * 16 * 32 = 4 * 12 * 52 8 * 12 * 32 = 4 * 20 * 44 8 * 16 * 28 = 4 * 28 * 36 8 * 18 * 26 = 6 * 16 * 46 8 * 20 * 24 = 8 * 12 * 48 12 * 14 * 26 = 6 * 20 * 42 12 * 20 * 20 = 8 * 16 * 44 14 * 18 * 20 = 6 * 28 * 34 7 * 20 * 26 = 7 * 13 * 47 6 * 12 * 36 = 6 * 10 * 50 6 * 20 * 28 = 6 * 14 * 46 6 * 21 * 27 = 7 * 12 * 47 13 * 14 * 27 = 7 * 20 * 39 13 * 20 * 21 = 7 * 26 * 33 5 * 20 * 30 = 5 * 15 * 45 4 * 14 * 38 = 6 * 8 * 50 4 * 20 * 32 = 4 * 16 * 44 4 * 24 * 28 = 8 * 8 * 48 8 * 10 * 38 = 6 * 12 * 46 8 * 12 * 36 = 4 * 28 * 32 8 * 22 * 26 = 10 * 12 * 42 10 * 14 * 32 = 6 * 22 * 36 12 * 16 * 28 = 8 * 20 * 36 12 * 18 * 26 = 10 * 16 * 38 12 * 20 * 24 = 8 * 24 * 32 16 * 18 * 22 = 10 * 20 * 34 16 * 20 * 20 = 12 * 16 * 36 3 * 20 * 34 = 3 * 17 * 43 2 * 20 * 36 = 2 * 18 * 42 2 * 27 * 29 = 4 * 9 * 49 6 * 23 * 29 = 8 * 13 * 41 10 * 19 * 29 = 12 * 13 * 37 11 * 18 * 29 = 9 * 20 * 33 11 * 20 * 27 = 9 * 22 * 31 16 * 19 * 23 = 13 * 18 * 31 1 * 20 * 38 = 1 * 19 * 41 8 * 20 * 32 = 12 * 12 * 36 12 * 12 * 36 = 8 * 20 * 32