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Let p >3 be a prime number. For each nonempty subset T of \{0,1,2,3, \ldots , p-1\}, let E(T) be the set of all (p-1)-tuples (x_1, \ldots ,x_{p-1} ), where each x_i \in T and x_1+2x_2+ \ldots + (p-1)x_{p-1} is divisible by p and let |E(T)| denote the number of elements in E(T). Prove that

|E(\{0,1,3\})| \geq |E(\{0,1,2\})|

with equality if and only if p = 5.

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