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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 700 mod 831 using the Extended Euclidean Algorithm:
nbqr t1t2t3
831700113101-1
7001315451-16
13145241-16-13
4541146-1319
414101-1319-203
414019-203831
Answer

So t = -203. Now we still have to apply mod n to that number:
-203 mod 831 ≡ 628
So the multiplicative inverse of 700 modulo 831 is 628.

Verification

Let i be the answer we just found, so i=628. We also have b=700 and n=831.
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) ≡
628 × 700 (mod 831) ≡
439600 (mod 831) ≡
1 (mod 831)