modular arithmatic help!

Find the inverse of 19 modulo 43.

Wait, so does that mean x=19(mod43)?

I guess x^43=(mod43), by one of euler theorems. But, then lol.

Anyway, how do you do that?

Also, solve 19x=17(mod43)?

That is all.

Reply 1

NegativeEpsilon

1

Assuming you are working additively, to find the inverse of 19 (mod 43), you want to solve

19 + x = 43 = 0 (mod 43) (and I'll let you work that one out for yourself :wink:

)

As to 19x=17 (mod 43), I would be lazy and do it by trial and error.

Reply 2

Simplicity

OP

17

NegativeEpsilon

Assuming you are working additively, to find the inverse of 19 (mod 43), you want to solve

19 + x = 43 = 0 (mod 43) (and I'll let you work that one out for yourself :wink:

)

As to 19x=17 (mod 43), I would be lazy and do it by trial and error.

Yes I know thow that but, how do you solve

-19+x=43=0(mod43)?

I'm a idiot, need more help.

Reply 3

davros

16

Is the second question supposed to follow on from the first? If so, you need the multiplicative inverse!

If you want the additive inverse I'm sure you can find a number x such that 19 + x = 43 as NegativeEpsilon says!!

Reply 4

Simplicity

OP

17

davros

Is the second question supposed to follow on from the first? If so, you need the multiplicative inverse!

If you want the additive inverse I'm sure you can find a number x such that 19 + x = 43 as NegativeEpsilon says!!

x=23?

Yes they are the same question.

Hmm, how do you do that?

Reply 5

starofale

6

As far as I am aware, you need to use an algorithm to find a modular multiplicative inverse.
If you have a Casio natural display calculator with a table function, I can tell you how to do it on that. Otherwise just search for a website that can do it for you (or make your own program)