MathDB
Problems
Contests
National and Regional Contests
India Contests
Postal Coaching
2011 Postal Coaching
4
Equation has integer solution
Equation has integer solution
Source:
December 31, 2011
number theory unsolved
number theory
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive integers for which
a
c
=
b
2
+
b
+
1
ac = b^2 + b + 1
a
c
=
b
2
+
b
+
1
Prove that the equation
a
x
2
ā
(
2
b
+
1
)
x
y
+
c
y
2
=
1
ax^2 - (2b + 1)xy + cy^2 = 1
a
x
2
ā
(
2
b
+
1
)
x
y
+
c
y
2
=
1
has an integer solution.
Back to Problems
View on AoPS