# 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:

a=
b=

#### Output

This is the output of the Extended Euclidean Algorithm using the numbers a=383 and b=527531:
abqr s1s2s3 t1t2t3
3835275310383101010
527531383137714001-1377101
38314021031-1377275501-2
140103137-13772755-41321-23
103372292755-413211019-23-8
372918-413211019-151513-811
2983511019-1515156472-811-41
8513-1515156472-7162311-4152
531256472-71623128095-4152-93
3211-71623128095-19971852-93145
2120128095-199718527531-93145-383

So we found that:

• gcd(383, 527531) = 1
• s = -199718
• t = 145

Verification
If our answer is correct, then the absolute value of `s × a + t × b` is equal to the `gcd` of `a` and `b`. We have:
• |`s × a + t × b`| = |-199718 × 383 + 145 × 527531| = |-76491994 + 76491995| = |1| = 1
• `gcd(a, b)` = gcd(383, 527531) = 1