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Eotvos Mathematical Competition (Hungary)
1931 Eotvos Mathematical Competition
1
1
Part of
1931 Eotvos Mathematical Competition
Problems
(1)
2/p can be expressed in exactly one way in the form 1/x+1/y
Source: Eotvos 1931 p1
9/10/2024
Let
p
p
p
be a prime greater than
2
2
2
. Prove that
2
p
\frac{2}{p}
p
2
can be expressed in exactly one way in the form
1
x
+
1
y
\frac{1}{x}+\frac{1}{y}
x
1
+
y
1
where
x
x
x
and
y
y
y
are positive integers with
x
>
y
x > y
x
>
y
.
number theory