diff --git a/math/euclidean_algorithm.wiki b/math/euclidean_algorithm.wiki new file mode 100644 index 0000000..cb2ebf4 --- /dev/null +++ b/math/euclidean_algorithm.wiki @@ -0,0 +1 @@ += Euclidean Algorithm = diff --git a/math/index.wiki b/math/index.wiki index 4d76bb2..394742b 100644 --- a/math/index.wiki +++ b/math/index.wiki @@ -10,4 +10,5 @@ The purest study of them all * [[prime]] * [[relative_prime]] -* +* [[modular_inverse]] +* [[euclidean_algorithm]] diff --git a/math/modular_inverse.wiki b/math/modular_inverse.wiki new file mode 100644 index 0000000..8a0f860 --- /dev/null +++ b/math/modular_inverse.wiki @@ -0,0 +1,26 @@ += Modular Inverse = + +A modular inverse is an _x_ such that satisfies the equation of form + +A * x = (mod m) + +This is derived from a statement in form + +A^-1 (mod m) + +This is due to the nature of modular operations, and can be shown via the +following set of steps. + +A^-1 = 1/A + +A * x = 1 + +x = 1/A + +Therefore, via substiution + +A * x = (mod m) + +This means that x will be the inverse of A + +To solve this, see the [[euclidean_algorithm]]