or polynomials (modulo m(x)), we must also introduce the corresponding concept of inverse polynomials. The inverse polynomial of a nonzero polynomial, p(x), is noted p-1(x) and is defined by the equivalent identities p-|(x)= p(x) mod m(x). We also know that the inverse exists because m(x) is irreducible, i.e., p(x) and m(x) do not have a common divider. As with modular arithmetic, the search for the inverse can be performed by the extended Euclidian algorithm (EEA). Let me explain the EEA through two representative examples: for instance, find (1) the inverse of 7 in modulus 39, i.e., the value of 7-1 mod 39 and (2) the inverse of 5 in modulus 16 272, i.e., the value of 5-1 mod 16 272. Considering example (1), Appendix Y Table Y1 Extended Euclidian algorithm to find 7-1 mod 39. 5 X 7 = 35 1 = 5 39 - 35 = 4 39 5 = 34 1 X 4 = 4 1 X 34 = 34 7 - 4 = 3 1 - 34 = -33 1 X 3 = 3 1 X (-33) = -33 4 - 3 = 1 34 - (-33) = 67 = 28 Table Y2 Extended Euclidian algorithm to find 5-1 mod 16 272. 16 272 16272 3254 X 5 = 16270 3254 X 1 = 3254 16272 - 16270 = 2 16272 - 3254 = 13 018 2 X 2 = 4 2 X 13 018 = 26036 5 - 4 = 1 1 - 26036 = -26035 the algorithm proceeds as shown in Table Y1, with the steps as numbered in the first column. In steps 1 and 2, we fill out the table as shown. We first divide 39 by 7, to find that the integer part of the result is [39/7] = 5. In step 3, we multiply line 2 by 5, and in step 4 we subtract the result of line 3 from that of line 1. This completes the first round. Consider next the ratio 7/4, whose integer part is [7/4] = 1. In step 5, we multiply the results of line 4 by 1, and in step 6, we subtract the result of line 5 from that of line 2. This completes the second round. Consider next the ratio 7/3, whose integer part is [4/3] = 1. In step 7, we multiply the results of line 6 by 1, and in step 8, we subtract the result of line 7 from that of line 4. If we have obtained 1 in the first column (line 8), we have finished. When positive, the number to the right is the inverse that we have been looking fo