Dear Monks!

The node The Oldest Plays the Piano inspired me a bit playing with regular expressions on numbers represented by '1'x$nr. Something works fine (see below: checking for "dividable by 5" or the famous prime-check). Unfortunately I don't manage to check if the number is a square - at least not with pure regexes (see my tries below) - and my google-Fu is not good enough to find a hint online.

Can you please enlighten me?
Thanks, Rata 

my $nr = 25;    my $n = 5-1; 
print "dividable by 5  :-)\n" if (1 x $nr) =~ /^(1+)\1{$n}$/;         
+     # works
print "prime\n"               if (1 x $nr) !~ /^(11+)\1+$/;           
+     # works
(1 x $nr) !~ /^(1+)(1*)$ (?{ sq($1)}) (0) /x;                         
+     # works - but not what I want ...
             sub sq  { print  "SQUARE\n"  if ((length($_[0]) * length(
+$_[0])) == $nr) ; }
             

my $len = 'length($1)-1';             
print "square2  :-)\n"        if (1 x $nr) =~ /^(1+)\1{$len}$/;       
+     # this won't work 
print "square3  :-)\n"        if (1 x $nr) =~ /^(1+)\1{length($1)-1}$/
+;    # this won't work .. but what will?!?!?!

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In reply to check for square-number with a regex by Ratazong

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