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32
Number of solutions for |x_1| + |x_2| +...+ |x_k| = n
Number of solutions for |x_1| + |x_2| +...+ |x_k| = n
Source: ILL 1979-32
June 2, 2011
combinatorics unsolved
combinatorics
Problem Statement
Let
n
,
k
≥
1
n, k \ge 1
n
,
k
≥
1
be natural numbers. Find the number
A
(
n
,
k
)
A(n, k)
A
(
n
,
k
)
of solutions in integers of the equation
∣
x
1
∣
+
∣
x
2
∣
+
⋯
+
∣
x
k
∣
=
n
|x_1| + |x_2| +\cdots + |x_k| = n
∣
x
1
∣
+
∣
x
2
∣
+
⋯
+
∣
x
k
∣
=
n
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