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How many perfect cubes lie between 2^8+1 and 2^18+1, inclusive?

Source: 2018 AMC 8 #25

November 20, 2018
AMC 82018 AMC 8

Problem Statement

How many perfect cubes lie between 28+12^8+1 and 218+12^{18}+1, inclusive?
<spanclass=′latex−bold′>(A)</span>4<spanclass=′latex−bold′>(B)</span>9<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>57<spanclass=′latex−bold′>(E)</span>58<span class='latex-bold'>(A) </span>4\qquad<span class='latex-bold'>(B) </span>9\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>57\qquad <span class='latex-bold'>(E) </span>58
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