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Find the two numbers

Source: 1971 AHSME Problem 14

April 19, 2014
algebradifference of squaresspecial factorizationsAMC

Problem Statement

The number (248−1)(2^{48}-1) is exactly divisible by two numbers between 6060 and 7070. These numbers are
<spanclass=′latex−bold′>(A)</span>61,63<spanclass=′latex−bold′>(B)</span>61,65<spanclass=′latex−bold′>(C)</span>63,65<spanclass=′latex−bold′>(D)</span>63,67<spanclass=′latex−bold′>(E)</span>67,69<span class='latex-bold'>(A) </span>61,63\qquad<span class='latex-bold'>(B) </span>61,65\qquad<span class='latex-bold'>(C) </span>63,65\qquad<span class='latex-bold'>(D) </span>63,67\qquad <span class='latex-bold'>(E) </span>67,69
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