text: Example For example, if the polynomial used to define the finite field GF(28) is , and  is the element whose inverse is desired, then performing the algorithm results in the computation described in the following table. Let us recall that in fields of order 2n, one has −z = z and z + z = 0 for every element z in the field). Since 1 is the only nonzero element of GF(2), the adjustment in the last line of the pseudocode is not needed.
  Thus, the inverse is , as can be confirmed by multiplying the two elements together, and taking the remainder by  of the result.
  The case of more than two numbers
  One can handle the case of more than two numbers iteratively.  First we show that .  To prove this let . By definition of gcd  is a divisor of  and .  Thus  for some .  Similarly  is a divisor of  so  for some .  Let . By our construction of ,  but since  is the greatest divisor  is a unit.  And since  the result is proven.
  So if   then there are  and  such that  so the final equation will be
  So then to apply to n numbers we use induction
  with the equations following directly.