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In this article we consider the most studied case of $\\mathbb{F}=\\mathbb{F}_{2^n}$.\n  A conjecture of Janwa-Wilson and McGuire-Janwa-Wilson (1993/1996), settled in 2011, was that the only exceptional monomial APN functions are the monomials $x^n$, where $n=2^i+1$ or $n={2^{2i}-2^i+1}$ (the Gold or the Kasami exponents respectively). 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