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Tuymaada Olympiad
1995 Tuymaada Olympiad
3
3
Part of
1995 Tuymaada Olympiad
Problems
(1)
(\sqrt5 +1)^{2x}+ (\sqrt5 -1)^{2x}=2^x(y^2+2) , infinite natural solutions
Source: Tuymaada 1995 p3
4/27/2019
Prove that the equation
(
5
+
1
)
2
x
+
(
5
−
1
)
2
x
=
2
x
(
y
2
+
2
)
(\sqrt5 +1)^{2x}+ (\sqrt5 -1)^{2x}=2^x(y^2+2)
(
5
+
1
)
2
x
+
(
5
−
1
)
2
x
=
2
x
(
y
2
+
2
)
has an infinite number of solutions in natural numbers.
Diophantine equation
algebra
number theory