Initial data commit

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

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+/*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= 500                                           /*use 500 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 multiply*/
+                      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. */