Bootstrap
  E.E.A. .com
It doesn't have to be difficult if someone just explains it right.

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 734839 mod 577 using the Extended Euclidean Algorithm:
nbqr t1t2t3
5777348390577010
7348395771273318101
577318125901-1
3182591591-12
25959423-12-9
59232132-920
2313110-920-29
13101320-2949
10331-2949-176
313049-176577
Answer

So t = -176. Now we still have to apply mod n to that number:
-176 mod 577 ≡ 401
So the multiplicative inverse of 734839 modulo 577 is 401.

Verification

Let i be the answer we just found, so i=401. We also have b=734839 and n=577.
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) ≡
401 × 734839 (mod 577) ≡
294670439 (mod 577) ≡
1 (mod 577)