MathDB

For positive integers

m

and

n

, let

f\left(m,n\right)

denote the number of

n

-tuples

\left(x_1,x_2,\dots,x_n\right)

of integers such that \left|x_1\right| \plus{} \left|x_2\right| \plus{} \cdots \plus{} \left|x_n\right|\le m. Show that f\left(m,n\right) \equal{} f\left(n,m\right).

Problem Statement