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National and Regional Contests
PEN Problems
PEN A Problems
84
84
Part of
PEN A Problems
Problems
(1)
A 84
Source:
5/25/2007
Determine all
n
∈
N
n \in \mathbb{N}
n
∈
N
for which [*]
n
n
n
is not the square of any integer, [*]
⌊
n
⌋
3
\lfloor \sqrt{n}\rfloor ^3
⌊
n
⌋
3
divides
n
2
n^2
n
2
.
floor function
Divisibility Theory