a brute force for the decimal case

  DB<34> sub dig { my @res= reverse split //,$_[0]; return @res,(0) x 
+4}


  DB<35> sub repeat { my %h; @h{@_}=(); return 1 if @_ > keys %h }


  DB<36> $d=4; $c=0; for $i (2..4) { for $x (1..10**$d) { $p = $i*$x+$
+c ; @x = dig($x); @p = dig($p); next if repeat($i,@x[0..$d-1], @p[0..
+$d]); next if $p[4]; print "($i * $x) + $c = $p \t $i \t @x[3,2,1,0] 
+\t@p[4,3,2,1,0]\n" }}
(4 * 1738) + 0 = 6952    4       1 7 3 8        0 6 9 5 2
(4 * 1963) + 0 = 7852    4       1 9 6 3        0 7 8 5 2
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