if ($string =~ /[^A-Z0-9]/) {
   # String contains a character other than A-Z, 0-9.
   ...
} else {
   # String only contains characters A-Z, 0-9.
   ...
}
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or

if ($string =~ /^[A-Z0-9]*\z/) {
   # String only contains characters A-Z, 0-9.
   ...
} else {
   # String contains a character other than A-Z, 0-9.
   ...
}
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#!/usr/bin/perl -l

use strict;
use warnings;

my $regexp = qr/^[^A-Z0-9]+$/;

print 'abc' =~ $regexp;
print 'ABC' =~ $regexp;
print 'ab0' =~ $regexp;
print '^|+' =~ $regexp;
print ''    =~ $regexp;
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