Question

\(3^-1 mod 59\)

how do negative exponents and modular arithmetic work?

Answer 1

3^-1 is the multiplicative inverse of 3 in mod 59

so you are looking for an x value that makes this equation true

3x = 1 (mod 59)

Answer 2

ah, so 3^-5 would be 3^5x?

Answer 3

what does it mean when it says \(3^{-5}\cong 20\)

Answer 4

mod 59, but that isn't important (I don't think)

Answer 5

we know that \(3^{-1}\) is \(\dfrac{1}{3}\)
in modulo \(59\) :

\[\dfrac{1}{3} = \dfrac{20}{60}\equiv \dfrac{20}{1} = 20\]

Answer 6

oh yeah, you showed me this trick a week ago

Answer 7

and so \(3^{-5}=(3^{-1})^5\)

Answer 8

which is congruent to 17, which is what my professor got.

awesome. thank you so much ganesh. sorry about being a jerk jim

Answer 9

and the other 2