MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2017 India National Olympiad
3
3
Part of
2017 India National Olympiad
Problems
(1)
Number of triples (x,a,b)
Source: INMO Problem 3
1/15/2017
Find the number of triples
(
x
,
a
,
b
)
(x,a,b)
(
x
,
a
,
b
)
where
x
x
x
is a real number and
a
,
b
a,b
a
,
b
belong to the set
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
}
\{1,2,3,4,5,6,7,8,9\}
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
}
such that
x
2
ā
a
{
x
}
+
b
=
0.
x^2-a\{x\}+b=0.
x
2
ā
a
{
x
}
+
b
=
0.
where
{
x
}
\{x\}
{
x
}
denotes the fractional part of the real number
x
x
x
.
algebra
floor function