Question

QUESTION 7 If modular n = 137, e = 100, what is the additive Inverse of

Answer 1

Given that

MODULAR = 137

and e= 100

So, we need find the additive inverse

we know that in modular arithmatic additive inverse of 'e' is nothing but a value y in such a way that e +y ≡ 0(mod n )

That implies the sum of additive inverses of a number is equivalent to 0 of mod n

If a number is given and the additive inverse of it is not known and themodular n is known ,we can find the additive inverse very easily.

For this first we need divide the moular n by the given number (e).

Then find the remainder of the above division.

Now the remainder that we get by dividing the modular n and the number whose additive inverse has to be found, is th eultimate additive inverse that we need.

So given n = 137

e = 100

let x= remainder obtained by the division of modular n and the number.

x= 137/100

quotient= 1

remainder =37

=>x=37

which further implies from the below equation

e +y ≡ 0(mod n )

x=y=37

where y is the additive inverse.

=>Now lets substitute all th evalues in the equation

e +y ≡ 0(mod n )

100+37 ≡ 0(mod 137)

Hence the equation is satisfied.

so the additive inverse of e is 37

verification:

100 + 37 = 137 .  

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