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Baltic Way
1994 Baltic Way
7
Numerator is divisible by p
Numerator is divisible by p
Source: Baltic Way 1994
December 22, 2011
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number theory proposed
number theory
Problem Statement
Let
p
>
2
p>2
p
>
2
be a prime number and
1
+
1
2
3
+
1
3
3
+
…
+
1
(
p
−
1
)
3
=
m
n
1+\frac{1}{2^3}+\frac{1}{3^3}+\ldots +\frac{1}{(p-1)^3}=\frac{m}{n}
1
+
2
3
1
+
3
3
1
+
…
+
(
p
−
1
)
3
1
=
n
m
where
m
m
m
and
n
n
n
are relatively prime. Show that
m
m
m
is a multiple of
p
p
p
.
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