sub test {
        print 
        $_[0] =~ $_[1]
        ? "matched\n"
        : "not matched\n";
}

$p2 = qr/(1{4})*/;
$p3 = qr/(1{9})*/;
$issquare = qr/^(1{4})*(1{9})*$/;

#for square numbers of form 2^2k * 3^2k
test(('1'x36), $issquare);#2^2*3^2 <-- perfect square
test(('1'x37), $issquare);#2^2*3^2+1 <-- not perfect square
test(('1'x324), $issquare);#2^2*3^4 <-- perfect square
test(('1'x325), $issquare);#2^2*3^4+1 <-- not perfect square
test(('1'x9216), $issquare);#2^10*3^4 <-- perfect square
test(('1'x9217), $issquare);#2^10*3^4+1 <-- not perfect square