Find $log_{g} (a) mod p$ for the following values of $p, g,$ and $a$. If $a$ is not a power of $g$, then $log_{g}(a) mod p =$ “undefined”. $a=4, g=3, p=11$
I was thinking $g^4=81=4=a,$ but I don't know how to calculate $log_{3}(4) mod 11$
Find $log_{g} (a)mod p$ for the following values of p, g, and a. If a is not a power of $g$, then $log_{g} (a)mod p=$ “undefined”. $a=4, g=3, p=11$
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discrete-mathematics
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0So it should be undefined. Thank you! I misunderstand the question. – 2017-02-24
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0I have converted my comment into an answer. You can accept the answer if it helped you. – 2017-02-24
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0Your thoughts: $$g^4 = 81 \equiv (a = 4) \pmod {11}.$$ are correct. So it is not undefined. – 2017-03-23
1 Answers
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Well, your question says that If a is not a power of g, then log g (a mod p) = “undefined” and 4 is not a power of 3, so $\implies ?$
Hope you can take it from here.
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0In the OP's first example I believe that the asker is showing that $a$ is a power of $g, \mod {11}$: That is $3^4 = 81 \equiv 4\pmod{11}$, when $g = 3,\;a=4,\; p =11$. So you can not dismiss it as undefined. – 2017-03-23