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For a polynomial in the finite field GF(28) where m(x) is the irreducible polynomial m(x) = x^8+x^4+x^3+x+1; calculate:

f(x) + g(x) mod m(x) over GF(2^8).                                                             

f(x) * g(x) mod m(x) over GF(2^8)

calculate gcd( f(x), g(x))

Pair 1                                                  Pair 2                                      

f(x) = x^7 + x                                       f(x) = x^6 + x^4 + x^3 + x^1        

g(x) = x^6 + x^3 + x^2 + x + 1               g(x) =x^6 + 1