# Calculator

For the Euclidean Algorithm, Extended Euclidean Algorithm and multiplicative inverse.

#### Before you use this calculator

If you're used to a different notation, the output of the calculator might confuse you at first.
Even though this is basically the same as the notation you expect. If that happens, don't panic.
Just make sure to have a look the following pages first and then it will all make sense:

#### Input

Algorithm

Choose which algorithm you would like to use.

Numbers

Enter the input numbers. Note that you need to enter n before b.
E.g. if you want to know the multiplicative inverse of 26 mod 11, then use n=11 and b=26.

n=
b=

#### Output

This is the calculation for finding the multiplicative inverse of 11 mod 1189 using the Extended Euclidean Algorithm:
nbqr t1t2t3
118911108101-108
1111101-1081189

So t = -108. Now we still have to apply mod n to that number:
-108 mod 1189 ≡ 1081
So the multiplicative inverse of 11 modulo 1189 is 1081.

Verification

Let i be the answer we just found, so i=1081. We also have b=11 and n=1189.
If our answer is correct, then `i × b (mod n) ≡ 1 (mod n)`.
Let's see if that's indeed the case.
i × b (mod n) ≡
1081 × 11 (mod 1189) ≡
11891 (mod 1189) ≡
1 (mod 1189)