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Romania Contests
Romania Team Selection Test
2000 Romania Team Selection Test
3
TST-Romania, 2000
TST-Romania, 2000
Source: binomial coefficient
October 15, 2009
number theory proposed
number theory
Problem Statement
Prove that for any positive integers
n
n
n
and
k
k
k
there exist positive integers
a
>
b
>
c
>
d
>
e
>
k
a>b>c>d>e>k
a
>
b
>
c
>
d
>
e
>
k
such that
n
=
(
a
3
)
±
(
b
3
)
±
(
c
3
)
±
(
d
3
)
±
(
e
3
)
n=\binom{a}{3}\pm\binom{b}{3}\pm\binom{c}{3}\pm\binom{d}{3}\pm\binom{e}{3}
n
=
(
3
a
)
±
(
3
b
)
±
(
3
c
)
±
(
3
d
)
±
(
3
e
)
Radu Ignat
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