#### oldtryingtorenew

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Can someone explain the following equation and how its been solved?

1= -14*43(mod 67)

43^-1 (mod 67) = -14

then the result is 53

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- Thread starter oldtryingtorenew
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Can someone explain the following equation and how its been solved?

1= -14*43(mod 67)

43^-1 (mod 67) = -14

then the result is 53

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Both side of the first identity are divided by 43 to get the second identity.

Can someone explain the following equation and how its been solved?

1= -14*43(mod 67)

43^-1 (mod 67) = -14

then the result is 53

As for the "result", [imath]53 \equiv -14 \mod 67[/imath], although I am not sure what "result" means in this context. Following the advice in post #2 might clear up my confusion

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If you found this work in some source, it will be very helpful if you show us that source (ideally as a link or an image). We want to see what they say they are doing. They are definitely not solving an equation, since there is no unknown.

Can someone explain the following equation and how its been solved?

1= -14*43(mod 67)

43^-1 (mod 67) = -14

then the result is 53

It appears that they are starting with a known fact, that [imath]1\equiv-14\cdot43(\text{mod }67)[/imath], which you can prove if you know what congruence mod 67 means; then they multiplied both sides by the multiplicative inverse of 43 (assuming it exists), to show that [imath]43^{-1}\equiv-14(\text{mod }67)[/imath]. (Note that the notation you show is incorrect.) Then we can guess that the "result" means that they have found that 53 is the least non-negative residue of -14 (by adding 67 to -14), and they are calling that the inverse of 43.

We don't know why they are doing this, or what you already understand, that we can use to explain it to you.