MathDB
Problems
Contests
National and Regional Contests
Vietnam Contests
Vietnam National Olympiad
2010 Vietnam National Olympiad
4
VMO 2010-Pro 4:Equation has at least n root
VMO 2010-Pro 4:Equation has at least n root
Source:
December 1, 2010
induction
number theory unsolved
number theory
Problem Statement
Prove that for each positive integer n,the equation
x
2
+
15
y
2
=
4
n
x^{2}+15y^{2}=4^{n}
x
2
+
15
y
2
=
4
n
has at least
n
n
n
integer solution
(
x
,
y
)
(x,y)
(
x
,
y
)
Back to Problems
View on AoPS