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National and Regional Contests
Greece Contests
Greece National Olympiad
2017 Greece National Olympiad
3
3
Part of
2017 Greece National Olympiad
Problems
(1)
Perfect Square
Source: 2017 Greece National Olympiad Problem 3
5/2/2017
Find all integer triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
with
a
>
0
>
b
>
c
a>0>b>c
a
>
0
>
b
>
c
whose sum equal
0
0
0
such that the number
N
=
2017
−
a
3
b
−
b
3
c
−
c
3
a
N=2017-a^3b-b^3c-c^3a
N
=
2017
−
a
3
b
−
b
3
c
−
c
3
a
is a perfect square of an integer.
algebra
number theory