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PEN S Problems
16
16
Part of
PEN S Problems
Problems
(1)
S 16
Source:
5/25/2007
Show that if
a
a
a
and
b
b
b
are positive integers, then
(
a
+
1
2
)
n
+
(
b
+
1
2
)
n
\left( a+\frac{1}{2}\right)^{n}+\left( b+\frac{1}{2}\right)^{n}
(
a
+
2
1
)
n
+
(
b
+
2
1
)
n
is an integer for only finitely many positive integer
n
n
n
.
modular arithmetic
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