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Korea National Olympiad
2022 Korea National Olympiad
8
8
Part of
2022 Korea National Olympiad
Problems
(1)
Equation on rational numbers
Source: KMO 2022 P8
10/29/2022
p
p
p
is a prime number such that its remainder divided by 8 is 3. Find all pairs of rational numbers
(
x
,
y
)
(x,y)
(
x
,
y
)
that satisfy the following equation.
p
2
x
4
ā
6
p
x
2
+
1
=
y
2
p^2 x^4-6px^2+1=y^2
p
2
x
4
ā
6
p
x
2
+
1
=
y
2
number theory
prime numbers