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In this paper, a proof is given that there does not exist a linearized polynomial $L(x)\in\mathbb{F}_{2^n}[x]$ such that x 驴驴驴1驴+驴L(x) is a permutation on $\mathbb{F}_{2^n}$ when n驴驴驴5, which is proposed as a conjecture in Li and Wang (Des Codes Cryptogr 58(3):259---269, 2011). As a consequence of this result, if a permutation is EA-equivalent to the inverse function over $\mathbb{F}_{2^n}$ , then it is affine equivalent to the inverse mapping when n驴驴驴5.