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National and Regional Contests
PEN Problems
PEN N Problems
17
N 17
N 17
Source:
May 25, 2007
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Problem Statement
Suppose that
a
a
a
and
b
b
b
are distinct real numbers such that
a
−
b
,
a
2
−
b
2
,
⋯
,
a
k
−
b
k
,
⋯
a-b, \; a^{2}-b^{2}, \; \cdots, \; a^{k}-b^{k}, \; \cdots
a
−
b
,
a
2
−
b
2
,
⋯
,
a
k
−
b
k
,
⋯
are all integers. Show that
a
a
a
and
b
b
b
are integers.
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