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Math Help - Fermatís Little Theorem Problem

  1. #1
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    Fermatís Little Theorem Problem

    Using Fermatís Little Theorem, or, otherwise, find the remainder when 3^203 is divided by 11. Thanks for your help in advance.
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  2. #2
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    Quote Originally Posted by MathStudent1 View Post
    Using Fermatís Little Theorem, or, otherwise, find the remainder when 3^203 is divided by 11. Thanks for your help in advance.
    11 does not divide 3.

    Thus,

    3^10 = 1 (mod 11)

    Thus,

    (3^10)^20 = 1^20 (mod 11)

    Thus

    3^200 = 1 (mod 11)

    Thus,

    3^203 = 3^3 = 27 = 5 (mod 11)
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  3. #3
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    TPH,

    Can you tell me how you went from 27 in the last line and then you got 5 from there? I understand the mod(11) part. Thanks!
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    Quote Originally Posted by MathStudent1 View Post
    TPH,

    Can you tell me how you went from 3^203 to 3^3 in the last line? Then I know 3^3 is 27 and then how did you get 5 from there? I understand the mod(11) part. Thanks!
    Okay, = is supposed to mean 'congruent to' instead of 'equals'.

    I multiplied both sides by 3^3. And then 3^3=27 and under mod 11 that is 5.
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  5. #5
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    Got it! Thanks.
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