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National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
1971 Dutch Mathematical Olympiad
3
diophantine x^2 + x +1 = y^2
diophantine x^2 + x +1 = y^2
Source: Netherlands - Dutch NMO 1971 p3
January 28, 2023
number theory
diophantine
Diophantine equation
Problem Statement
Prove that
(
0
,
1
)
(0,1)
(
0
,
1
)
,
(
0
,
−
1
)
(0, -1)
(
0
,
−
1
)
,
(
−
1
,
1
)
( -1,1)
(
−
1
,
1
)
and
(
−
1
,
−
1
)
(-1,-1)
(
−
1
,
−
1
)
are the only integer solutions of
x
2
+
x
+
1
=
y
2
.
x^2 + x +1 = y^2.
x
2
+
x
+
1
=
y
2
.
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