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4
S 4
S 4
Source:
May 25, 2007
quadratics
induction
binomial coefficients
algebra
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Problem Statement
If
x
x
x
is a real number such that
x
2
−
x
x^2 -x
x
2
−
x
is an integer, and for some
n
≥
3
n \ge 3
n
≥
3
,
x
n
−
x
x^n -x
x
n
−
x
is also an integer, prove that
x
x
x
is an integer.
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