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UW Math Hour Olympiad 2014 Grades 8-10 #7

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June 2, 2014
floor functionmodular arithmeticMath Hour Olympiad

Problem Statement

If aa is any number, ⌊a⌋\lfloor a \rfloor is aa rounded down to the nearest integer. For example, ⌊π⌋=\lfloor \pi \rfloor = 33. Show that the sequence
⌊2117⌋\lfloor \frac{2^{1}}{17} \rfloor, ⌊2217⌋\lfloor \frac{2^{2}}{17} \rfloor, ⌊2317⌋\lfloor \frac{2^{3}}{17} \rfloor, …\dots
contains infinitely many odd numbers.
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