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The parameters $(q,r,a)$ for which $f$ is a permutation polynomial (PP) of ${\\Bbb F}_{q^2}$ have been determined in the following cases: (i) $a^{q+1}=1$; (ii) $r=1$; (iii) $r=3$. These parameters together form three infinite families. For $r>3$ (there is a good reason not to consider $r=2$) and $a^{q+1}\\ne 1$, computer search suggested that $f$ is not a PP of ${\\Bbb F}_{q^2}$ when $q$ is not too small relative to $r$. In the present paper, we prove that this claim is true. 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