# 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 527531 mod 383 using the Extended Euclidean Algorithm:
nbqr t1t2t3
3835275310383010
5275313831377140101
383140210301-2
1401031371-23
10337229-23-8
3729183-811
29835-811-41
851311-4152
5312-4152-93
321152-93145
2120-93145-383

So t = 145. Now we still have to apply mod n to that number:
145 mod 383 ≡ 145
So the multiplicative inverse of 527531 modulo 383 is 145.

Verification

Let i be the answer we just found, so i=145. We also have b=527531 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) ≡
145 × 527531 (mod 383) ≡
76491995 (mod 383) ≡
1 (mod 383)