OpenStudy (anonymous):

How would you do 5^-1 (mod 26) ?

5 years ago
OpenStudy (anonymous):

what is mod 26

5 years ago
OpenStudy (anonymous):

modulo

5 years ago
OpenStudy (anonymous):

5 to the negative first powwer is .2 or one fifth

5 years ago
OpenStudy (anonymous):

Don't worry. I know that much.

5 years ago
OpenStudy (anonymous):

o well sry because i dont understand what modulo is.

5 years ago
OpenStudy (anonymous):

snivy

5 years ago
OpenStudy (jim_thompson5910):

5^-1 is the multiplicative inverse of 5

5 years ago
OpenStudy (jim_thompson5910):

So you're looking for the value k that satisfies the equation 5k = 1 (mod 26)

5 years ago
OpenStudy (jim_thompson5910):

Notice how 5*5 = 25 = -1 (mod 26) So 5*(-5) = -5*5 = -25 = -(-1) = 1 (mod 26) So this means that k = -5 = 21 (mod 26) And that 5^-1 = 21 (mod 26)

5 years ago
OpenStudy (anonymous):

for the 5*5, was it a guess and check kind of thing or is there a way to derive that?

5 years ago
OpenStudy (jim_thompson5910):

mostly guess and check, you can see that 26 is near 25 which makes the guessing not so bad (with different numbers, more guesses are needed)

5 years ago
OpenStudy (anonymous):

Which 5 is the 5 in 5^1? or is that unnecessary?

5 years ago
OpenStudy (jim_thompson5910):

I'm not sure where you're pointing to, can you elaborate?

5 years ago
OpenStudy (anonymous):

|dw:1337653972385:dw|

5 years ago