Question

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

Answer 1

what is mod 26

Answer 2

modulo

Answer 3

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

Answer 4

Don't worry. I know that much.

Answer 5

o well sry because i dont understand what modulo is.

Answer 6

snivy

Answer 7

5^-1 is the multiplicative inverse of 5

Answer 8

So you're looking for the value k that satisfies the equation

5k = 1 (mod 26)

Answer 9

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)

Answer 10

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

Answer 11

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)

Answer 12

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

Answer 13

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