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Lusophon Mathematical Olympiad
2020 Lusophon Mathematical Olympiad
2
2
Part of
2020 Lusophon Mathematical Olympiad
Problems
(1)
2017 and a (quadratic) equation
Source: Lusophon Math Olympiad 2020 Day 1 #2
11/1/2020
a) Find a pair(s) of integers
(
x
,
y
)
(x,y)
(
x
,
y
)
such that:
y
2
=
x
3
+
2017
y^2=x^3+2017
y
2
=
x
3
+
2017
b) Prove that there isn't integers
x
x
x
and
y
y
y
, with
y
y
y
not divisible by
3
3
3
, such that:
y
2
=
x
3
ā
2017
y^2=x^3-2017
y
2
=
x
3
ā
2017
number theory
quadratics