# 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 948 mod 383 using the Extended Euclidean Algorithm:
nbqr t1t2t3
3839480383010
9483832182101
38318221901-2
182199111-219
191118-219-21
1181319-2140
8322-2140-101
321140-101141
2120-101141-383

So t = 141. Now we still have to apply mod n to that number:
141 mod 383 ≡ 141
So the multiplicative inverse of 948 modulo 383 is 141.

Verification

Let i be the answer we just found, so i=141. We also have b=948 and n=383.
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) ≡
141 × 948 (mod 383) ≡
133668 (mod 383) ≡
1 (mod 383)