Finding the greatest common divisor + Bézout's identity. I use Ruby's built in function.

gcd.rb

def gcd(a, b)
  return a if b == 0
  return b if a == 0
  a.gcd(b)
end

def bezout(a, b)
  return 1, 0 if b == 0
  q, r = a.divmod b
  s, t = bezout(b, r)
  return t, s - q * t
end

puts "Input two numbers to find the Greatest Common Divisor."
puts "Bonus: Bézout's identity is provided."

z = 0
while z == 0
  i = gets.to_i
  j = gets.to_i
  puts gcd(i, j)
  puts bezout(i, j)

  puts "Calculate again? 1/2"
  z = gets.to_i
  if z == 1 then
    z = 0
  elsif z == 2 then
    z = z+1
  else
    puts "Undefined."
  end
end