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Topic: Congruence Question
Replies: 2   Last Post: Oct 24, 2012 1:05 PM

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Ben Brink

Posts: 197
From: Rosenberg, TX
Registered: 11/11/06
RE: Congruence Question
Posted: Oct 24, 2012 6:50 AM
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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





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