September 2017 Update

Task/Multiplicative-order/REXX/multiplicative-order.rexx

@@ -0,0 +1,26 @@
+/*REXX pgm computes multiplicative order of a minimum integer  N  such that  a^n mod m≡1*/
+wa=0; wm=0     /*       ═a═   ══m══     */       /*maximum widths of the A and M values.*/
+@.=.;              @.1=   3      10
+                   @.2=  37    1000
+                   @.3=  37   10000
+                   @.4=  37    3343
+                   @.5=  37    3344
+                   @.6=   2    1000
+pad=left('',9)
+d=100                                            /*use 100 decimal digits for a starter.*/
+     do w=1  for 2                               /*when W≡1, find max widths of A and M.*/
+       do j=1  while @.j\==.;  parse var @.j a . 1 r m , n
+       if w==1  then do;  wa=max(wa, length(a));   wm=max(wm, length(m));   iterate;   end
+       if m//a==0  then n= ' [solution not possible]'     /*test co-prime for  A and B. */
+       numeric digits d                          /*start with  100  decimal digits.     */
+       if n==''  then do n=2;     p=r*a          /*compute product──may have an exponent*/
+                      parse  var  p  'E'  _      /*try to extract the exponent from  P. */
+                      if _\==''   then do;  numeric digits _+d  /*bump the decimal digs.*/
+                                            p=r*a               /*recalculate integer P.*/
+                                       end
+                      if p//m==1  then leave     /*now, perform the nitty-gritty modulo.*/
+                      r=p                        /*assign product to  R  for next mult. */
+                      end   /*n*/                /* [↑]    //   is really  ÷  remainder.*/
+       say pad  'a='  right(a,wa)  pad  "m=" right(m,wm)  pad  'multiplicative order:'   n
+       end   /*j*/
+     end     /*w*/                               /*stick a fork in it,  we're all done. */