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    I am trying to find (11^298)(mod31), the answer to which is 10 but I keep in getting 6.
    Here is my working:
    (11^298)(mod31) = (11^2)^149 (mod31) = (29^149)(mod31) = (29^2)^74*29(mod31) = (4^74)*29(mod31) = 2^148*29(mod31) = (2^5)^29*(2^3)*29(mod31) = 2^3*29(mod31) = 232(mod31) = 6
    Thank you in advance!
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    Your first error is going from (11^2)^149 to 29^149 (11^2 = 28 mod 31, NOT 29).

    Edit: You would also make your life a lot easier if you used Fermat's Little Theorem to reduce the exponent before you start calculations.
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    (Original post by DFranklin)
    Your first error is going from (11^2)^149 to 29^149 (11^2 = 28 mod 31, NOT 29).

    Edit: You would also make your life a lot easier if you used Fermat's Little Theorem to reduce the exponent before you start calculations.
    Thank you! Unfortunately, we have not studied Fermat's Little Theorem
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    (Original post by spacewalker)
    Thank you! Unfortunately, we have not studied Fermat's Little Theorem
    Oh. I wouldn't be too happy if I had to do all that number crunching. :lol:

    Anyway, 10 is good. Hope it worked out in the end.
 
 
 
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Updated: February 7, 2017

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