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2
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2013 APMO
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(1)
Floor of square root
Source: APMO 2013, Problem 2
5/3/2013
Determine all positive integers
n
n
n
for which
n
2
+
1
[
n
]
2
+
2
\dfrac{n^2+1}{[\sqrt{n}]^2+2}
[
n
]
2
+
2
n
2
+
1
is an integer. Here
[
r
]
[r]
[
r
]
denotes the greatest integer less than or equal to
r
r
r
.
modular arithmetic
inequalities
quadratics
function
algebra
floor function
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