This is the part of the program it comes from. I thought all the math stuff would be Math::Something so I didn't know about that combinatorics module! That sounds very interesting. I wonder if/how it could be applied here? It runs through all the possible polynomials of a certain form and spits out the ones whose derivatives have (approximately) integer roots.

# $lep means smallest nonzero root in the interval [0, $rep]
# $rep means right endpoint of the interval [0, $rep]
my $lep = int 1;
my $rep = int 100;

foreach my $x ($lep+2 .. $rep ) {
    foreach my $y ($lep+1 .. $x-1 ) {
        foreach my $z ($lep .. $y-1 ) {
            foreach my $s (1..$rep/4) {
                unless ($y == $x + $s && $z == $y + $s ) {

                    # assigns a truth value to whether or not it is wi
+thin 0.0001 of an integer (1=true, 0=false)
                    sub is_approximately_an_integer {
                    my $eps = 0.0001;
                    while( my $w = shift ) {
        
                        # need to use "round", "int" does not work!
    
                        return 0 if abs( $w-round($w) ) > $eps;
                        }
                        return 1
                    }
                }
            }
     
            push @wants,
            map { { join(', ', $x, $y, $z) => $_ } }
                grep { is_approximately_an_integer( @$_ ) } [
                    poly_roots(
                        poly_derivative(
                            
                            # expanded form of x*(x - $x)*(x - $y)*(x 
+- $z)
                            1, -$x - $y - $z, $x*$y + $x*$z + $y*$z, -
+$x*$y*$z, 0
                        )
                    )       
                ];
        }
    }
}
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