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For positive integers mmm and nnn, let f(m,n)f(m, n)f(m,n) denote the number of nnn-tuples (x1,x2,…,xn)(x_1, x_2, \dots , x_n)(x1,x2,…,xn) of integers such that ∣x1∣+∣x2∣+⋯+∣xn∣≤m|x_1|+|x_2|+ \cdots +|x_n| \leq m∣x1∣+∣x2∣+⋯+∣xn∣≤m. Show that f(m,n)=f(n,m)f(m, n) = f(n, m)f(m,n)=f(n,m).
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