MathDB
Problems
Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2017 Hanoi Open Mathematics Competitions
10
x^2-2ax+b=0,x^2- 2bx+c=0, x^2-2cx+a=0, integer roots (HOMC 2017 J Q10)
x^2-2ax+b=0,x^2- 2bx+c=0, x^2-2cx+a=0, integer roots (HOMC 2017 J Q10)
Source:
August 7, 2019
trinomial
Integer
roots
algebra
Problem Statement
Find all non-negative integers
a
,
b
,
c
a, b, c
a
,
b
,
c
such that the roots of equations:
{
x
2
−
2
a
x
+
b
=
0
x
2
−
2
b
x
+
c
=
0
x
2
−
2
c
x
+
a
=
0
\begin{cases}x^2 - 2ax + b = 0 \\ x^2- 2bx + c = 0 \\ x^2 - 2cx + a = 0 \end{cases}
⎩
⎨
⎧
x
2
−
2
a
x
+
b
=
0
x
2
−
2
b
x
+
c
=
0
x
2
−
2
c
x
+
a
=
0
are non-negative integers.
Back to Problems
View on AoPS