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3
P 3
P 3
Source:
May 25, 2007
function
algebra
floor function
Additive Number Theory
pen
Problem Statement
Prove that infinitely many positive integers cannot be written in the form
x
1
3
+
x
2
5
+
x
3
7
+
x
4
9
+
x
5
11
,
{x_{1}}^{3}+{x_{2}}^{5}+{x_{3}}^{7}+{x_{4}}^{9}+{x_{5}}^{11},
x
1
3
+
x
2
5
+
x
3
7
+
x
4
9
+
x
5
11
,
where
x
1
,
x
2
,
x
3
,
x
4
,
x
5
∈
N
x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\in \mathbb{N}
x
1
,
x
2
,
x
3
,
x
4
,
x
5
∈
N
.
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