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    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.
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    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 )

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

    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.
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    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!!
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    (Original post by 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?
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    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)
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    (Original post by Simplicity)
    x=23?

    Yes they are the same question.

    Hmm, how do you do that?
    To find the multiplicative inverse, you need to find a number a such that

    19a=1 mod 43

    Just use trial and error to find a.
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    19a = 1 mod 43 <=> 19a+43x = 1 (Hint: Euclidean algorithm)
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    aops has a huge section on mod arithmetic if you have a look perhaps you will benefit?
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    (Original post by SimonM)
    19a = 1 mod 43 <=> 19a+43x = 1 (Hint: Euclidean algorithm)
    Hmm, thanks. But, lol how can you solve 19a+43x=1.

    So a=-9, which is a=34?

    Can you do that, as I was under the impression that -9=32(mod43)?

    (Original post by DeanK22)
    aops has a huge section on mod arithmetic if you have a look perhaps you will benefit?
    I will look through the website to find some.
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    (Original post by Simplicity)
    Hmm, thanks. But, lol how can you solve 19a+43x=1
    Euclidean Algorithm, as the hint suggested :p:

    43 = 19.2 + 5
    19 = 5.3 + 4

    etc.
 
 
 
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