# 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 358871 mod 563 using the Extended Euclidean Algorithm:
nbqr t1t2t3
5633588710563010
358871563637240101
56324028301-2
240832741-25
837419-25-7
749825-761
9241-761-251
212061-251563

So t = -251. Now we still have to apply mod n to that number:
-251 mod 563 ≡ 312
So the multiplicative inverse of 358871 modulo 563 is 312.

Verification

Let i be the answer we just found, so i=312. We also have b=358871 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) ≡
312 × 358871 (mod 563) ≡
111967752 (mod 563) ≡
1 (mod 563)