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Prime Quadratic Roots

Source:

February 11, 2008
quadraticsVietaalgebranumber theoryprime numbersspecial factorizations

Problem Statement

Both roots of the quadratic equation x^2 \minus{} 63x \plus{} k \equal{} 0 are prime numbers. The number of possible values of k k is <spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> <spanclass=′latex−bold′>morethanfour</span> <span class='latex-bold'>(A)</span>\ 0 \qquad <span class='latex-bold'>(B)</span>\ 1 \qquad <span class='latex-bold'>(C)</span>\ 2 \qquad <span class='latex-bold'>(D)</span>\ 3 \qquad <span class='latex-bold'>(E)</span>\ <span class='latex-bold'>more than four</span>
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