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Task/Modular-inverse/8th/modular-inverse.8th

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+\ return "extended gcd" of a and b; The result satisfies the equation:
+\     a*x + b*y = gcd(a,b)
+: n:xgcd \ a b --  gcd x y
+  dup 0 n:= if
+    1 swap            \ -- a 1 0
+  else
+    tuck n:/mod
+    -rot recurse
+    tuck 4 roll
+    n:* n:neg n:+
+  then ;
+
+\ Return modular inverse of n modulo mod, or null if it doesn't exist (n and mod
+\ not coprime):
+: n:invmod \ n mod -- invmod
+  dup >r
+  n:xgcd rot 1 n:= not if
+    2drop null
+  else
+    drop dup 0 n:< if r@ n:+ then
+  then
+  rdrop ;
+
+42 2017 n:invmod . cr bye