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2012 District Olympiad
1
\sqrt{a^2_1+a^2_2+ ...+a^2_{2012}-1} is irrational 2012 Romania District VII p1
\sqrt{a^2_1+a^2_2+ ...+a^2_{2012}-1} is irrational 2012 Romania District VII p1
Source:
September 1, 2024
algebra
number theory
irrational number
Problem Statement
Let
a
1
,
a
2
,
.
.
.
,
a
2012
a_1, a_2, ... , a_{2012}
a
1
,
a
2
,
...
,
a
2012
be odd positive integers. Prove that the number
A
=
a
1
2
+
a
2
2
+
.
.
.
+
a
2012
2
−
1
A=\sqrt{a^2_1+ a^2_2+ ...+ a^2_{2012}-1}
A
=
a
1
2
+
a
2
2
+
...
+
a
2012
2
−
1
is irrational.
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