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A power mapping f(x)=x/sup d/ over GF(p/sup n/) is said to be differentially k-uniform if k is the maximum number of solutions x/spl isin/GF(p/sup n/) of f(x+a)-f(x)=b where a, b/spl isin/GF(p/sup n/) and a/spl ne/0. A 2-uniform mapping is called almost perfect nonlinear (APN). We construct several new infinite families of nonbinary APN power mappings.