The following works (note the lack of curly braces in the back-reference):

use strict;

foreach ( "123  123 ", "1 1 ", "45 &45 " ) {
    print( "\"$_\"\n  " );
    if ( /^(\d+?) (.\1) / ) {
        printf( "Match 1 => \"%s\", Match 2 => \"%s\"\n",
                $1, $2 );
    } else {
        print( "No match\n" );
    }
}
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Outputs:

"123  123 "
  Match 1 => "123", Match 2 => " 123"
"1 1 "
  No match
"45 &45 "
  Match 1 => "45", Match 2 => "&45"
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Update: corrected spelling in sentence.