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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 5219 mod 641 using the Extended Euclidean Algorithm:
nbqr t1t2t3
64152190641010
5219641891101
641917401-7
9142231-7155
4311-7155-162
3130155-162641
Answer

So t = -162. Now we still have to apply mod n to that number:
-162 mod 641 ≡ 479
So the multiplicative inverse of 5219 modulo 641 is 479.

Verification

Let i be the answer we just found, so i=479. We also have b=5219 and n=641.
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) ≡
479 × 5219 (mod 641) ≡
2499901 (mod 641) ≡
1 (mod 641)