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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 8412 mod 505 using the Extended Euclidean Algorithm:
nbqr t1t2t3
50584120505010
841250516332101
505332117301-1
33217311591-12
173159114-12-3
159141152-335
14524-335-73
541135-73108
4140-73108-505
Answer

So t = 108. Now we still have to apply mod n to that number:
108 mod 505 ≡ 108
So the multiplicative inverse of 8412 modulo 505 is 108.

Verification

Let i be the answer we just found, so i=108. We also have b=8412 and n=505.
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) ≡
108 × 8412 (mod 505) ≡
908496 (mod 505) ≡
1 (mod 505)