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Putnam
1960 Putnam
B4
B4
Part of
1960 Putnam
Problems
(1)
Putnam 1960 B4
Source: Putnam 1960
6/11/2022
Consider the arithmetic progression
a
,
a
+
d
,
a
+
2
d
,
…
a, a+d, a+2d,\ldots
a
,
a
+
d
,
a
+
2
d
,
…
where
a
a
a
and
d
d
d
are positive integers. For any positive integer
k
k
k
, prove that the progression has either no
k
k
k
-th powers or infinitely many.
Putnam
arithmetic sequence
powers