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Canada Contests
Canada National Olympiad
1998 Canada National Olympiad
1
1
Part of
1998 Canada National Olympiad
Problems
(1)
[x] equation
Source: Canada 1998
3/4/2006
Determine the number of real solutions
a
a
a
to the equation:
[
1
2
a
]
+
[
1
3
a
]
+
[
1
5
a
]
=
a
.
\left[\,\frac{1}{2}\;a\,\right]+\left[\,\frac{1}{3}\;a\,\right]+\left[\,\frac{1}{5}\;a\,\right] = a.
[
2
1
a
]
+
[
3
1
a
]
+
[
5
1
a
]
=
a
.
Here, if
x
x
x
is a real number, then
[
x
]
[\,x\,]
[
x
]
denotes the greatest integer that is less than or equal to
x
x
x
.
number theory unsolved
number theory