MathDB
Minimum Integer Value

Source:

January 5, 2009
number theoryprime factorization

Problem Statement

Let x x and y y be positive integers such that 7x^5 \equal{} 11y^{13}. The minimum possible value of x x has a prime factorization acbd a^cb^d. What is a \plus{} b \plus{} c \plus{} d? <spanclass=′latex−bold′>(A)</span> 30<spanclass=′latex−bold′>(B)</span> 31<spanclass=′latex−bold′>(C)</span> 32<spanclass=′latex−bold′>(D)</span> 33<spanclass=′latex−bold′>(E)</span> 34 <span class='latex-bold'>(A)</span>\ 30 \qquad <span class='latex-bold'>(B)</span>\ 31 \qquad <span class='latex-bold'>(C)</span>\ 32 \qquad <span class='latex-bold'>(D)</span>\ 33 \qquad <span class='latex-bold'>(E)</span>\ 34
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