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a \in (1,9) such (a - 1/a) is an integer (HOMC 2010 J Q4)

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July 25, 2019
number theoryInteger

Problem Statement

How many real numbers a∈(1,9)a \in (1,9) such that the corresponding number a−1aa- \frac1a is an integer?
(A): 00, (B): 11, (C): 88, (D): 99, (E) None of the above.
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