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Baltic Way
2007 Baltic Way
16
16
Part of
2007 Baltic Way
Problems
(1)
s can be written as a fraction with denominator coprime to 6
Source: Baltic Way 2007
11/30/2010
Let
a
a
a
and
b
b
b
be rational numbers such that
s
=
a
+
b
=
a
2
+
b
2
s=a+b=a^2+b^2
s
=
a
+
b
=
a
2
+
b
2
. Prove that
s
s
s
can be written as a fraction where the denominator is relatively prime to
6
6
6
.
modular arithmetic
number theory
relatively prime
number theory proposed