clark:~/Desktop jim$ ./egypt.pl 19/20
19/20 = 1/2 + 1/3 + 1/9 + 1/180

clark:~/Desktop jim$ ./egypt.pl 18/20
18/20 = 1/2 + 1/3 + 1/15


##</code><code>##


sub egypt {my$f=2;do{return(--$f,egypt($_[0]/$f))unless$_[0]%$f++}
while$_[0]>1}print"$ARGV[0] = ",join(' + ',pharaoh(hiero(split '/',
$ARGV[0]))),"\n";sub hiero{my(%nf,%df);$nf{$_}++for egypt(shift);++
$df{$_}for egypt(shift);do{($df{$_},$nf{$_})=($df{$_}-$nf{$_},$nf{$_}
-$df{$_})if$df{$_}}for keys%nf;return(eval join('*',1,(map{($_)x
$nf{$_}}keys%nf)),eval join('*',1,(map{($_)x$df{$_}}keys%df)))}sub
pharaoh {return$_[0]==1?"$_[0]/$_[1]":("1/".(int($_[1]/$_[0])+1),
pharaoh(hiero($_[0]*(int($_[1]/$_[0])+1)-$_[1],$_[1]*(int($_[1]/
$_[0])+1))))}


##</code><code>##


sub egypt {
	my $f = 2;
	do {return (--$f, egypt($_[0] / $f)) unless $_[0] % $f++} while
	$_[0] > 1;
}

print "$ARGV[0] = " , join(
		' + ',
		pharaoh(hiero(split '/', $ARGV[0]))
	), "\n";

sub hiero {
	my (%nf, %df);
	
	$nf{$_}++ for egypt(shift);
	$df{$_}++ for egypt(shift);
	
	do {($df{$_}, $nf{$_}) = ($df{$_} - $nf{$_}, $nf{$_} - $df{$_})
	if $df{$_} } for keys %nf;
	
	return (eval join('*', 1, (map {($_) x $nf{$_}} keys %nf)),
			eval join('*', 1, (map {($_) x $df{$_}} keys %df)));
}

sub pharaoh {
	return $_[0] == 1 ? "$_[0]/$_[1]" : ( "1/" . (int($_[1] / 
	$_[0]) + 1), pharaoh(hiero($_[0] * (int($_[1] / $_[0]) + 1) - 
	$_[1], $_[1] * (int($_[1] / $_[0]) + 1))))
}


##</code><code>##


sub egypt {
	my $f = 2;
	do {return (--$f, egypt($_[0] / $f)) unless $_[0] % $f++} while
	$_[0] > 1;
}


##</code><code>##


print "$ARGV[0] = " , join(
		' + ',
		pharaoh(hiero(split '/', $ARGV[0]))
	), "\n";



##</code><code>##

sub hiero {
	my (%nf, %df);
	
	$nf{$_}++ for egypt(shift);
	$df{$_}++ for egypt(shift);
	
	do {($df{$_}, $nf{$_}) = ($df{$_} - $nf{$_}, $nf{$_} - $df{$_})
	if $df{$_} } for keys %nf;
	
	return (eval join('*', 1, (map {($_) x $nf{$_}} keys %nf)),
			eval join('*', 1, (map {($_) x $df{$_}} keys %df)));
}

##</code><code>##

sub pharaoh {
	return $_[0] == 1 ? "$_[0]/$_[1]" : ( "1/" . (int($_[1] / 
	$_[0]) + 1), pharaoh(hiero($_[0] * (int($_[1] / $_[0]) + 1) - 
	$_[1], $_[1] * (int($_[1] / $_[0]) + 1))))
}