Solving Some Affine Equations over Finite Fields
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Let l and k be two integers such that l|k. Define T_l^k(X):=X+X^p^l+...+X^p^l(k/l-2)+X^p^l(k/l-1) and S_l^k(X):=X-X^p^l+...+(-1)^(k/l-1)X^p^l(k/l-1), where p is any prime. This paper gives explicit representations of all solutions in p^n to the affine equations T_l^k(X)=a and S_l^k(X)=a, a∈p^n. For the case p=2 that was solved very recently in <cit.>, the result of this paper reveals another solution.
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