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Two Relatively Prime Integers

Source: 2012 AMC10A Problem #17

February 8, 2012
quadraticsnumber theoryrelatively primealgebraquadratic formulaAMC

Problem Statement

Let aa and bb be relatively prime integers with a>b>0a>b>0 and a3−b3(a−b)3=733\tfrac{a^3-b^3}{(a-b)^3}=\tfrac{73}{3}. What is a−ba-b?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 5 <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ 5
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