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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
37
37
Part of
PEN A Problems
Problems
(1)
A 37
Source:
5/25/2007
If
n
n
n
is a natural number, prove that the number
(
n
+
1
)
(
n
+
2
)
⋯
(
n
+
10
)
(n+1)(n+2)\cdots(n+10)
(
n
+
1
)
(
n
+
2
)
⋯
(
n
+
10
)
is not a perfect square.
number theory
greatest common divisor
modular arithmetic
relatively prime
Divisibility Theory