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PEN G Problems
28
G 28
G 28
Source:
May 25, 2007
Irrational numbers
Problem Statement
Do there exist real numbers
a
a
a
and
b
b
b
such that [*]
a
+
b
a+b
a
+
b
is rational and
a
n
+
b
n
a^n +b^n
a
n
+
b
n
is irrational for all
n
∈
N
n \in \mathbb{N}
n
∈
N
with
n
≥
2
n \ge 2
n
≥
2
? [*]
a
+
b
a+b
a
+
b
is irrational and
a
n
+
b
n
a^n +b^n
a
n
+
b
n
is rational for all
n
∈
N
n \in \mathbb{N}
n
∈
N
with
n
≥
2
n \ge 2
n
≥
2
?
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