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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 6060 mod 701 using the Extended Euclidean Algorithm:
nbqr t1t2t3
70160600701010
60607018452101
701452124901-1
45224912031-12
249203146-12-3
203464192-314
461928-314-31
1982314-3176
8322-3176-183
321176-183259
2120-183259-701
Answer

So t = 259. Now we still have to apply mod n to that number:
259 mod 701 ≡ 259
So the multiplicative inverse of 6060 modulo 701 is 259.

Verification

Let i be the answer we just found, so i=259. We also have b=6060 and n=701.
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) ≡
259 × 6060 (mod 701) ≡
1569540 (mod 701) ≡
1 (mod 701)