require 'rational'

def n_fact(p, q)
	$n = p * q
	print "N = ", $n, "\n"
	
	$l = (p-1).lcm(q-1)
	print "L = ", $l, "\n"
	
	$e = 1
	continue_e = true
	while continue_e do
		$e += 1
		if $e.gcd($l) == 1 then
			print "E = ", $e, "\n"
			continue_e = false
		end
	end
	
	$d = 1
	continue_d = true
	while continue_d do
		$d += 1
		if $e * $d % $l == 1 then
			print "D = ", $d, "\n"
			continue_d = false
		end
	end
end

def e(p)
	p p**$e % $n
end

def d(c)
	p c**$d % $n
end