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Example

For example, if the polynomial used to define the finite field GF(2) is p = x + x + x + x + 1, and a = x + x + x + 1 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 2, 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 x + x + x + x, as can be confirmed by multiplying the two elements together, and taking the remainder by p of the result.