MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1999 Moldova Team Selection Test
13
13
Part of
1999 Moldova Team Selection Test
Problems
(1)
find the number of solutions of a flool function equation
Source:
4/10/2011
Let
N
N
N
be a natural number. Find (with prove) the number of solutions in the segment
[
1
,
N
]
[1,N]
[
1
,
N
]
of the equation
x
2
−
[
x
2
]
=
(
x
−
[
x
]
)
2
x^2-[x^2]=(x-[x])^2
x
2
−
[
x
2
]
=
(
x
−
[
x
]
)
2
, where
[
x
]
[x]
[
x
]
means the floor function of
x
x
x
.
function
algebra
floor function
algebra unsolved