# 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 841 mod 563 using the Extended Euclidean Algorithm:
nbqr t1t2t3
5638410563010
8415631278101
5632782701-2
27873951-279
7512-279-81
522179-81241
2120-81241-563

So t = 241. Now we still have to apply mod n to that number:
241 mod 563 ≡ 241
So the multiplicative inverse of 841 modulo 563 is 241.

Verification

Let i be the answer we just found, so i=241. We also have b=841 and n=563.
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) ≡
241 × 841 (mod 563) ≡
202681 (mod 563) ≡
1 (mod 563)