(Prior to publication, this paper should be cited as arXiv:1407.4567.)

We determine the factorization of   X· f(X) - Y·g(Y) in  K[X,Y]  for all squarefree additive polynomials f,g in K[X] and all fields K of odd characteristic. This answers a question of Kaloyan Slavov, who needed these factorizations to prove a result in his paper arXiv:1410:3701 concerning an algebraic-geometric analogue of the Kakeya problem.

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