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Ben Brink
Posts:
198
From:
Rosenberg, TX
Registered:
11/11/06


RE: Congruence Question
Posted:
Oct 24, 2012 6:50 AM



Edward, In #1, your idea of adding/subtracting multiples of 9 (k +/ 9m for k = 0, 1, ..., 8 and m any integer) is solid. Have forgotten Fermat's Little Theorem so will leave that for others. Thanks, Ben
> Date: Tue, 23 Oct 2012 20:52:38 0400 > From: discussions@mathforum.org > To: discretemath@mathforum.org > Subject: Congruence Question > > So now I'm moving on and learning about congruence for the first time. Trying to take it all in and did some example problems to sharpen my skills, but I have two questions. > > List all congruence classes for congruence mod 9, giving the most usual and one other name for each. Is this right? > > 27 18 9 0 9 18 27 36 45 54 63 72 81 90 > 26 17 8 1 10 19 28 37 46 55 64 73 82 91 > 25 16 7 2 11 20 29 38 47 56 65 74 83 92 > 24 15 6 3 12 21 30 39 48 57 66 75 84 93 > 23 14 5 4 13 22 31 40 49 58 67 76 85 94 > 22 13 4 5 14 23 32 41 50 59 68 77 86 95 > 21 12 3 6 15 24 33 42 51 60 69 78 87 96 > 20 11 2 7 16 25 34 43 52 61 70 79 88 97 > 19 10 1 8 17 26 35 44 53 62 71 80 89 98 > > 2.Use Fermat's Little Theorem to compute > 3^508 (mod 509), 3^509(mod 509) and 3^512 (mod 509) > > Any ideas for question 2? I'm lost



