MathDB
Problems
Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
1987 Canada National Olympiad
5
5
Part of
1987 Canada National Olympiad
Problems
(1)
Show that [√(4n + 2)] = [√(4n + 3)] = [√n + √(n + 1)]
Source:
10/3/2011
For every positive integer
n
n
n
show that
[
4
n
+
1
]
=
[
4
n
+
2
]
=
[
4
n
+
3
]
=
[
n
+
n
+
1
]
[\sqrt{4n + 1}] = [\sqrt{4n + 2}] = [\sqrt{4n + 3}] = [\sqrt{n} + \sqrt{n + 1}]
[
4
n
+
1
]
=
[
4
n
+
2
]
=
[
4
n
+
3
]
=
[
n
+
n
+
1
]
where
[
x
]
[x]
[
x
]
is the greatest integer less than or equal to
x
x
x
(for example
[
2.3
]
=
2
[2.3] = 2
[
2.3
]
=
2
,
[
π
]
=
3
[\pi] = 3
[
π
]
=
3
,
[
5
]
=
5
[5] = 5
[
5
]
=
5
).