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31
O 31
O 31
Source:
May 25, 2007
induction
ratio
LaTeX
geometric sequence
Problem Statement
Prove that, for any integer
a
1
>
1
a_{1}>1
a
1
>
1
, there exist an increasing sequence of positive integers
a
1
,
a
2
,
a
3
,
⋯
a_{1}, a_{2}, a_{3}, \cdots
a
1
,
a
2
,
a
3
,
⋯
such that
a
1
+
a
2
+
⋯
+
a
n
∣
a
1
2
+
a
2
2
+
⋯
+
a
n
2
a_{1}+a_{2}+\cdots+a_{n}\; \vert \; a_{1}^{2}+a_{2}^{2}+\cdots+a_{n}^{2}
a
1
+
a
2
+
⋯
+
a
n
∣
a
1
2
+
a
2
2
+
⋯
+
a
n
2
for all
n
∈
N
n \in \mathbb{N}
n
∈
N
.
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