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# Modular Arithmetic Question watch

1. 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
2. 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.
3. (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
4. (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.

Anyway, 10 is good. Hope it worked out in the end.

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Updated: February 7, 2017
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