MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
19
19
Part of
PEN A Problems
Problems
(1)
A 19
Source:
5/25/2007
Let
f
(
x
)
=
x
3
+
17
f(x)=x^3 +17
f
(
x
)
=
x
3
+
17
. Prove that for each natural number
n
≥
2
n \ge 2
n
≥
2
, there is a natural number
x
x
x
for which
f
(
x
)
f(x)
f
(
x
)
is divisible by
3
n
3^n
3
n
but not
3
n
+
1
3^{n+1}
3
n
+
1
.
induction
modular arithmetic
LaTeX
Divisibility Theory
number theory