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There exist several positive integers x such that 1/(x^2+x) is a terminating decimal. What is the second smallest such integer?

 Jun 4, 2018
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There exist several positive integers x such that 1/(x^2+x) is a terminating decimal.

What is the second smallest such integer?

 

The terminating decimal is if and only if the denominator has powers of only 2 and/or 5.

\(\begin{array}{|r|r|l|} \hline x & x^2+x & factor \\ \hline 1 & 2 & = 2^1 \checkmark \\ 2 & 6 & = 2 \cdot 3^1 \\ 3 & 12 & = 2^2 \cdot 3^1 \\ 4 & 20 & = 2^2\cdot 5^1 \checkmark \\ \hline \end{array}\)

 

The second smallest  positive integer x is 4

 

laugh

 Jun 4, 2018
edited by heureka  Jun 4, 2018

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