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More Notions

• x divides y if x*z = y for some z:

  x | y : <=> exists z: x*z = y .

• The greatest common divisor of x and y is the largest number that divides both x and y:

  gcd(x, y) := such z: z | x /\  z | y /\  (forall w: (w | x /\  w | y) => w <= z).

• The least common multiple of x and y is the smallest number that both x and y divide:

  lcm(x, y) := such z: x | z /\  y | z /\  (forall w: (x | w /\  y | w) => z <= w).