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Baltic Way
2002 Baltic Way
3
Find all sequences
Find all sequences
Source: Baltic Way 2002
November 13, 2010
induction
logarithms
algebra proposed
algebra
Problem Statement
Find all sequences
0
≤
a
0
≤
a
1
≤
a
2
≤
…
0\le a_0\le a_1\le a_2\le \ldots
0
≤
a
0
≤
a
1
≤
a
2
≤
…
of real numbers such that
a
m
2
+
n
2
=
a
m
2
+
a
n
2
a_{m^2+n^2}=a_m^2+a_n^2
a
m
2
+
n
2
=
a
m
2
+
a
n
2
for all integers
m
,
n
≥
0
m,n\ge 0
m
,
n
≥
0
.
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